Me and my opponent will be arguing which Pokémon in the video game series is the best, based on stats, overall fighting ability, etc.
1. No legendaries.
2. The Pokémon can be in gens I-VI. (Starting in Red/Blue and ending in X & Y), however all sequels are included for the purposes of updated stats (OR & AS).
3. No mega-evolutions (however Pokémon that can use Mega Evolution are still eligible as long as they don't have Mega-Evolution).
4. No trolling.
5. A forfeit results in an automatic loss.
6. You will choose the Pokémon and give it a viable moveset (so no Roar of Time Magikarps) and 1 item.
7. Have fun!
The Pokémon I choose is Aegislash. I await an opponent.
I thank Tminusfour20 for accepting! (Love the name by the way)
Aegislash, using its Stance Change, can manipulate its form on the field of battle.
Shield Mode provides high defensive capabilities with relatively low attack.
Sword Mode provides high attack capabilities with relatively low defense. 
Assuming this Espeon has ghost/dark type moves (which is more than plausible), the defense capabilities of Aegis will still be relatively high. While not being able to withstand much, both parties are at an inherent disadvantage, as the others' Pokemon's type or moves are the weakness of the other. 
Espeon's main advantage is in special attack, with little nothing else, except probably speed, which doesn't matter much later on.
To further illustrate my point I introduce DAMAGE CALCULATION! 
Here is the formula to illustrate damage:
Damage = ((((2 * Level / 5 + 2) * AttackStat * AttackPower / DefenseStat) / 50) + 2) * STAB * Weakness/Resistance * RandomNumber / 100
It seems complicated at first glance, but it's relatively easy to understand once you get the hang of it.
I'll take an example of Espeon's most powerful move against Aegis (Shadow Ball) and plug it in to Shield Form Aegis here. Assuming levels are 100 and random number is 100, we plug it in. As well, the stat for the Pokemon is at its lowest possible. I'll do the same for highest possible.
So we now have:
Damage = ((((2 * 100 / 5 + 2) * 238 * 80 / 274) / 50) + 2) * 1 * 2 * 100 / 100 = ~121 damage, which is 2 shadow balls to take down a minimum HP Aegis.
Timid Nature(+Speed, -Atk)
252 Speed/ 252 SpA /4 Spd
I'd Like to start off with Espeons Ability.
Magic Bounce allows the user to reflect all non damaging moves, hazards, and status moves. The rarity of this ability shoes just how powerful it is. At any point in time you can predict an enemy during a competitive battle will throw a thunder wave or will-o-wisp at you. This will be easily deflected by magic bounce even on switch in and an easily back fire on your opponent and can even send back stealth rock/spikes/toxic spikes/sticky web etc. This makes mid game switch ins a breeze for this Pokemon especially when you can properly anticipate your opponents next move. If in the case that you incorrectly predict and you take damage you can rest assure that focus sash will allow Espeon to survive and has the speed to deliver the first blow every round from one of three high coverage move sets.
Shadowball: Protects from Ghosts and other Psychic Types
Signal Beam: Protects from Dark/Psychic/Grass
Stored Power: STAB move with powerful potential
Strong against Fighting/Poison
My typical exploitation of Espeon's power is by boosting his stats usually indirectly through a baton pass from another Pokemon on the team. By boosting his stats stored power receives Base:20 + n(20). N being the number of stat boosts he possesses. Espeon has the move calm mind which adds a stat boost both to his SpA and his SpD adding to not only his ridiculous amount of SpA but also to the base power of the move stored power. After using calm mind once, stored power's base power will be at [20+2(20)]1.5 (The 1.5 comes from STAB as Stored Power is a Psychic Move. While this may seem minor at first, given enough chance to power up or the opportunity for a teammate to boost its power and baton pass to Espeon, for example a smeargle with geomancy/baton pass/spore. Geomancy Boosts SpA/SpD/speed by +2. that is 6 power boosts and can truly unleash the potential of stored power.
[20+6(20)]1.5= Base Power 210 !!! After Espeon gets baton passed in with this stat boost he is pretty much undef-eatable. He is fast enough to always hit first. If stored power doesn't kill you one of his other movies definitely will. He is guaranteed to survive at least one attack because of his held item. He is also unable to be statused confused or affecting in any way due to magic bounce.
While a 1 on 1 battle with Aegislash would probably give victory to Aegislash has a few Faults in his set up.
Your Aegislash set up is very prone to crippling. A Faster Pokemon with will-o-wisp would destroy your whole plan.
Stance Change prevents you from preparing for priority moves from faster opponents. If you are using Shadow Sneak and Greninja uses shadow sneak Greninja's shadow sneak will move first every time because of his speed. Also because he will always move first your stance change will be triggered by shadow sneak bringing you to attack mode and leaving you very weak to a shadow sneak attack by a faster opponent. The same strategy would probably work for a slower Pokemon as well now that I think of it.
The problem with King's Shield as a move is that while it may protect from damage, you are still vulnerable to a status move. There are also quite a few Pokemon who know Will-o-wisp as well as shadow sneak which would cut your attack power rendering a swords dance boosted shadow sneak powerful still but not nearly as powerful as it could be. He would slowly lose health and constantly be beaten in speed by a faster ghost type pokemon who also knows shadow sneak, god forbid the Pokemon has an infiltrator ability as well. Your Aegislash is set up to be a dominant sweeper but with all dominant sweepers he can easily be taken down with everything but brute force.
Reasons Espeon is a Better Pokemon:
A. High Special Attack and Speed ensures a powerful first strike almost every time
B. His power potential in perfect scenarios can completely change the course of the game at any given opportunity.
C. Strategic power of Magic Bounce and Stored Power for almost any situation
I thank opponent for his response. Sorry I wasn't able to respond earlier, as I was under time constraints. I'm typing this all with 4 hours left, please forgive me.
I think opponent and I are arguing different fronts here. It seems opponent is going for a more team-centered composition when I am simply talking about raw potential in terms of against the Espeon. Nonetheless, I shall refute.
I. Wide Range of Attacks
While the Espeon opponent provides has a wide range of attacks against opponents, opponent's entire build focuses on SpA and Speed, while mine focuses on Attack and Sp.Def, with 4 in HP. The only attack my Aegislash offers is physical based, while Sp.Atk is useful against most attacks by Pokémon, as a majorty of high-damage dealing moves are Sp.Atk. So it's a natural sweeper. Even with the focus sash, if Aegislash substitutes enough, and pulls off enough King's shields, it can totally deplete Shadow Ball's PP, as opponent has admitted to having no PP gain, and Aegis can infinitely Sub and King's Shield. If opponent decides to use Calm Mind, Aegis can pull off a Shadow Sneak while Substituted, and immediately switch back to King's Shield. This is the versatility this set offers.
As well, assume Aegis does a Shadow Sneak (leaving it in sword mode), then Espeon performs a SB. Here's the damage totals.
Damage = ((((2 * 100 / 5 + 2) * 394 * 80 / 218) / 50) + 2) * 1 * 2 * 100 / 100 = ~246 damage. While this would render my Aegis extremely low, there isn't a nature to hinder its HP and it has 4 EVs in HP, so it should go above the minimum HP level for an Aegis. This allows for 2 shadow sneaks, able to take out my opponent's Espeon easily with some HP to spare. This renders Espeon's FS useless in this scenario. If properly executed, even a small attack from another Pokemon renders this item useless, as it only needs to take 1 hit before it loses its value. Aegis always has value with his build setup.
II. Ability as a Wall
As based on Aegislash's defenses, he is immune to 3 types and resistant to 9 types of damage, being weak to 4 and normally damaged by 2. [1 from R2]
Take this as opposed to Espeon, who is damaged normally by 13 types, weak to 3, resistant to 2, and immune to none. [2 from R2]
As well, Aegislash, in Shield Form, can take a load of hits. King's Shield and Substitute help a lot at wasting the opponent's PP, trying to attack Aegislash. Aegis is able to hold off against a lot more than Espeon can. It doesn't matter about the super effective coverage. While still helpful, Aegislash is naturally immune to lots of other types, and can hold off normally, and combined with King's Shield and Substitute Aegislash can last an extremely long time.
Aegislash, while primarily designed to be a sweeper, is more than capable of being a wall in the build. With abilities such as Shield Form, King's Shield, and Substitute, even if Aegis cannot deal much damage, he is able to withstand a ton, and waste the opponent's PP. Even if his dmg isn't viable, he is a perfect wall, unlike Espeon, who relies on attacking fast and hard. If left with no defense, it is very susceptible to damage and able to be taken care of.
III. Status Effects
While Aegis is relatively prone to status effects, keep in mind his ability as a wall will not be hindered. He can still effectively Sub & King's Shield, and keep his defenses up extremely high. As well, paralysis doesn't even effect him that much, as one of its detriments is to cause the afflicted Pokemon to move slower, yet Aegislash almost always moves last anyway. Any burn, poison etc. can simply be taken by Substitute.
IV. Baton Pass
Dropped, as any Pokemon can take advantage from BP. (See video)
V. Opponent's Build.
Opponent, while seemingly having a build to cover all his weaknesses, forgets that his Defense, Sp. Def, and HP are extremely low. As well, he seem to cover all of his weak points (which is a good thing), but Espeon takes normal damage from multiple types.
With the proper capability, Aegislash is able to have a huge offensive and defensive advantage, while opponent's is primarily in offense and speed. While good, Speed is almost useless against an Aegislash as said Aegis will move slowly anyway.
Reasons Aegislash wins:
Aegislash has naturally superior stats.
Aegislash can function as a sweeper and a wall, as the Espeon purely relies on pure damage.
Aegislash is naturally immune to more types of attacks, and Espeon is relatively vulnerable to more as opposed to Aegis.
[1 from R2]
[2 from R2]
Tminusfour20 forfeited this round.
Hopefully opponent will be able to make one last refutation before the debate ends.
I extend, and I thank opponent for the debate.