Just like Iron Man and Peter Quill, Spider-Man is primarily a comedic, fun character and when needed, will get serious. RDJ is a comedic actor, so is Chris Pratt, and either guy can get dramatic at the right moments.
We've seen Dylan O'Brien do that in both Maze Runner and the latter of Teen Wolf season 3B, he'll do it once again in Scorch Trials.
I've never seen Asa do comedy, so I can't judge him on that front, but from what I have seen of him in interviews and such, he just seems very stiff, wooden, and awkward. He seems like a nice guy and is regarded by many as an up and coming star with great acting abilities. I agree. But just because he's a great actor... It does not necessarily mean he has what it takes to pull off Spider-Man/Peter Parker. Eric Stolz is a great actor and he didn't have it takes to pull off Marty McFly... Nuff said.
Don't forget Chris Evans, known more for humorous roles, completely toned down that side of himself for Cap.



