Cars, tracks and handling: Much wider choice of cars in Project CARS.
Concerning handling, some cars in Project CARS feel like you're driving in arcade racer, some feel undriveable (wheelspining all over the place), some are balanced and fun to drive, while in Assetto Corsa most, if not all cars feel like understeering during corner entrance, no grip at all. Thus both games don't have "the perfect handling", its up to your driving style, really.
Much Wider choice of tracks in Project CARS, however not all of them are laser scanned like in Assetto Corsa, they still look pretty good, but some are innacurate compared to the real ones.
Drifting in Assetto Corsa is much better, Project CARS attemps to drift just don't feel as realistic, but its still fun.
Graphics, looks & Weather: Hands down, Project CARS graphics are simply amazing, the cars look better, the tracks look better, the weather system has no rival in any sim racing game, it's also worth mentioning thats its extremly fun when you drive in rain, which lacks in Assetto Corsa. Don't get me wrong, Assetto Corsa overall graphics and looks are very good indeed, but certainly behind Project CARS.
It's also important to note that damage models in Project CARS are impressive, while on the other hand, they're extremly broken in Assetto Corsa.
Career: From what i seen so far Project CARS career mode is more in-depth than Assetto Corsa, although i don't plan on playing it.
A.I.: A.I. is much better in Project CARS, they are extremly broken in Assetto Corsa and even unable to overtake.
Multiplayer: Project CARS provides much better multiplayer comapred to Assetto Corsa, where the netcode is extremly broken, so competetive racing is out of the picture. Huge minus - neither have multi-class racing.
Physics: Honestly, both have very questionable physics, Assetto Corsa feels more connected to the road, though.
Force feedback: FFB in Project CARS is far behind Assetto Corsa, you don't feel that connected to the road as you should.
Customization: Project CARS doesn't yet provide much customization, unlike Asetto Corsa, which has HUGE modding community, which is really big advantage of the last one, for now.
Optimization: Project CARS has TERRIBLE optimization for AMD graphics cards, you'll end up running the game with 40 fps on ultra with high-end GPU. Assetto Corsa has much better optimization.
Conclusion and overall racing experience: Overall both games have rushed, unfinished feeling to them... Project CARS has very mixed personality concerning car handling and Assetto Corsa so far is only a hot lap simulator, as you can't experience any real racing(A.I. can't overtake, multiplayer racing is completely out of the picture). Multiplayer racing in Project CARS is fun and for the small time i played it i had amazing wheel to wheel battles, which again, is impossible in Assetto Corsa.
In the end both have a lot of pros and cons and although they both fall into the simulator racing genre they provide very different experiences, it's completely up to you which one fits you better.