There are many factors that can make either race the victor. But lets paint a picture. A flat battle ground with the elves standing opposite of the dwarves. The two fantasy powerhouses charging against each other in a battle that only has room for one victor. Dwarves are known for their blacksmithing skills which would mean that their armor and melee weapons would be unmatched. The elves on the other hand are know mainly for their archery, which means that by the time that the dwarves get to the elves, half of them would be already eliminated. It would be a epic battle of course and i'm not saying by any means that the dwarves don't have a battle plan, but dwarves are also very well know for being stubborn. I could honestly write a book about a battle like this and it would be a very very long book. But ultimately, i would have to make the elves win because i see their potential, even though i like dwarves more than i like elves.
The new Hobbit film greatly illustrates how inferior dwarves are to elves. The dwarves seem helpless, only surviving through luck rather than skill, whereas the elves seem invincible with their kung-fu skills, chopping of heads left and right where they go (run/fly/float/soar/cartwheel/etc). Of course, in another story (film) the skills might have been more equally distributed among elves and dwarves ;)
Well, I Lord Graesil shu Aln de Alanai en Saeron, would use magic to silence my dwarves opponent, causing him to be unable to use his runic magic against me. At this point, my foe would most likely try and use a ranged weapon, probably a crossbow. To defeat this, I would cut the string with a throwing knife, and most likely make a dent in his armor in the process. Having no more options, my enemy would probably take out his crush damage melee weapon. I would use my superior elven speed to dodge the slow, brute attacks, and draw close enough to stab at the gap in his helm. If this does not kill my opponent, he will be too injured to fight at normal capacity, and would be easily defeated.
Supposing that this is indeed a battle between the two races, I think that many of you fail to take into account the advantages that the dwarves have over elves as well as the advantages the elves have.
Equipment. The dwarves are known for their skills in a forge and their skill is regarded as unparalleled. So assuming the dwarves are superior in this field, it will give them the advantage of their weapons and armour being more effective. Meanwhile, whilst I do not deny the fact that the elves are brilliant craftsmen, their armour is designed so they can hop around, so they provide less protection against attacks.
Note that the dwarves have archers and sorcerers as well as the elves. And these dwarves have been trained to handle these weapons and so cannot be assumed to fire with no discipline and without hitting a single targets whilst you presume that the elves would hit the dwarves at their weakest link and instantly kill the dwarf with every arrow. And so if we're counting the number of dead before the two sides clash, I doubt that the difference will be as great as you all make it out to be.
In terms of personality, whilst generalisations can be made for all races, that does not mean to say that every dwarf and elf acts in this way. A dwarven general would not be as stubborn and hot-headed as others may be. Again, let's not be racist! These dwarves have been trained in the field of strategy and are nor liable to just send their troops charging at random. And dwarven soldiers would be disciplined just as the soldiers of any army, including elves. Vice versa, elves can be as stubborn and as impulsive as a dwarf can. These traits are not restricted to dwarves.
Whilst the elves may have a slight upper hand before any confrontation, it's at this stage that the dwarf takes the upper hand. Against brute strangth, aility and precision are inferior in close combat. Whilst the elves can dodge the dwarven attacks for quite some while, all it takes is a single blow to take out an elf whereas it would take more than one slash to bring down a heavily armoured dwarf. And at this stage, the dwarf is almost always triumphant.
But I would like to point out that almost all of the above points could be disregarded if you take strategy and terrain into account. And without being racist towards either race, a great military leader can come from both races.
It is unfair to use the the elves and dwarves in the new Hobbit film as comparable: When the dwarves escape Mirkwood, the dwarves have but a couple of weapons between all of them, are in barrels so have very limited movement and control, no armour and are being ambushed. So no, they're not winning purely by skill but that's unfair as they are NOT warriors but brave volunteers.
From Tolkein to D&D to WoW and Warhammer Dwarves, they are all about the same in terms of size and depiction. I have a bias, I admit, playing a Dwarf on WoW and in games like Baldur's Gate 2 and any of the great isometric D&D games of the mid-90s and early-2000s, but elves and half-elves always fascinated me, that aside...
Open field, flat ground would be a nightmare for just about any army facing a dwarven army. Imagine the 300 Spartans, but with centuries of fighting experience (depending on the verse, some dwarven races live as long or longer than certain elven races. Each can clock-in an average of 500 years esp the ones that see a lot of battle. How many of the immortal elves fell in Tolkein's world? Only immortal in their aging, really....Anyway...) Dwarves are typically stronger than humans, the D&D and WoW versions most definitely are, the WoW dwarves are as strong as the Tauren! (Bull Race, similar to Minotaurs in size and strength)....They have bonuses against fighting giants in D&D. They are so strong that they can strike up at opponents, a foot up, sometimes higher, and retain their punching power....
AS a former a boxer I can tell you that punching-up = a nightmare for someone who is a puncher, you lose power exponentially, it's simple physics.
Dwarves would be able to tank most kinds of arrows the Elves would throw at them. With no high ground it'd be hard to penetrate their shield-wall. Their armor could handle Elven blades, and when swords meet armor the swords tend to fail. Dwarves carry swords, axes, and hammers. Hammers are meant to destroy armor. Axes often have pike-like features on the ends and can penetrate armor. Elves would have spears, daggers, and a mixture of single-edged curved swords to regular longswords. All good for getting in-between the weak spots in armor if you're a good fighter.
In the end the shield-wall technique the dwarves form would take out the elves who are much better at guerilla tactics.
If you were to put this battle in a forest with the dwarven army having to deal with Elves hitting-and-running from the trees and brush, it'd be VERY difficult for generals of equal-skill to defeat the Elves in that scenario.
First off dwarves have much better armor, shields, and hand to hand weapons than the elves do I believe( Although I'm willing to admit the elves have more agility and better archers.) Most likely, the elves would unleash a couple of volleys at the dwarves, but considering their discipline, heavy armor, and superb shield formations I do not think the casualties would be heavy. Then we would have a large force of heavily armored dwarf shock troopers with spears crashing and crushing right through elven ranks in which the first several elven lines would break. We would then have an equally challenging hand to hand combat in which the dwarves could counterattack with another armored charge therefore crushing elven ranks.
Same example flat ground the dwarves and elves on either side of the field. If I was the dwarves general I would put my heaviest infantry in the front so even if the elves use their arrows they would pretty much bounce off the dwarven heavy units and I would have light skirmishers armed with spears and swords while using light armour and they are covered for the most part from the arrows because the dwarven heavy units will be taking the brunt of the arrow volleys. So they heavy units reach the elves and take out the most experienced elven soldiers with the intent of creating a break within the elven line so the light skirmishers can charge forward to eliminate the stragglers fleeing the battle. That's what I feel I would do as the dwarven general so that's just one possibility I'm not saying the dwarves are unbeatable I'm just saying against the elves they will usually win but if the elven general gets smart and flanks the dwarves and attack them from the rear then the dwarves would lose.