The puzzles in Professor Layton almost always have nothing to do with the plot and are just random obstacles that you need to solve. In Ace Attorney however, The game's gameplay and story go together perfectly making the game more immersive. The narrative and characters presented in Ace Attorney are also stronger whereas the Layton games are riddled with one dimensional characters and many plotholes. These aren't issues that Ace Attorney completely avoids but it at least keeps them to a minimum.
I've always been more of a scenario thinker. That is to say, I've always had a better time thinking a certain case over a longer period of time, rather than thinking of an answer on your feet. That is what I think sets these two series apart. Professor Layton focuses more on small puzzles that rarely have to do with the overall story, while Ace Attorney puts multiple pieces of information together to build a case and eventually solve the mystery. Plus, it's pretty damn fun to yell "OBJECTION!" into the DS mic!
I love both series, however they have vastly different ideas. Both games use logic and reasoning. However the gameplay is fundamentally different. In order to complete, well, pretty much anything in Professor Layton you need to solve small puzzles. In Ace Attorney you need to listen to the witnesses and use your evidence to counter. Also there's a very annoying investigation part. As you can see, both video games have vastly different ideas, and I like them both.
Both games are amazing for three reasons. One, both train your brain in critical thinking. Two both have awesome stories. Three, both have wonderful music. But if there's one thing of those three that Layton excels more in it is the critical thinking. Now many people would say "but the thinking required in phoenix wright is more advanced logic and me doing well a it makes me feel better". Well that's all fine and good but in phoenix wright just like the young attorney you can just bluff through it all with trial, error, and lots of saving and restarting. Yes in Layton you've got your hint coins and your multiple choice puzzles but there are several puzzles where guesswork would take ages. Lastly, even though I love both games as two of my favorite series's the best way to a gamer's heart is through nostalgia, and because Wright games are teen rated games one can't as easily become a child-hood fan. On the other hand Layton games are kid friendly, start out easy and are puzzle games making parents love them for their kids it is much easier for a nostalgia for layton games to be developed. So for all the reasons one would consider Wright games better there are also reasons for Layton games to be better, so even if they truly are equal more people can and will love the Professor Layton series just as I have for years.