There are advantages and disadvantages to them being with one or the other... yes, under Marvel, you probably would get a little more comic book accuracy and classic stories. I also agree with others that under Fox, while not perfect, they have developed a cinematic universe that has given most of us something special AND set the bar for team superhero movies.
Marvel movies have a tone that I, noticed I said "I", don't believe would serve the X-men well but, of course, Marvel is not able to depict the X-men, so we really don't know how they would do. Fox, IMO, needs fresh blood to come in and give the X-men a fresh perspective.
I believe that both studios, if they come to an agreement, could create a co-universe of sorts where the X-men and Avengers could crossover which would only serve both sides and would topple most, if not all, the biggest blockbusters of all time.