It is a debate that will be going on for quite some time. Marvel, easily the biggest name in comics, was in a bit of financial trouble some years ago and as a result, a ton of the character rights were sold off to separate movie studios. One of the biggest successes of these films is Fox's X-Men franchise. The franchise that has been around for 15 long years is Marvel Studios direct competition at the moment.
After multiple failed attempts to re-acquire these character rights, Marvel and Fox have accumulated a bit of bad blood. This has sparked a huge rivalry which led to Marvel killing off both the X-Men and the Fantastic Four in Marvel Comics. Most of the actors haven't said much pertaining to this conflict but James McAvoy recently commented on the issue in an interview with HeyUGuys and claimed Fox's dominance! Skip to 3:14 for McAvoy's comments!
There really isn't any competition?
According to James McAvoy, there is no competition simply because they do it better. While McAvoy will undoubtably support his own franchise, there definitely is a very high level of competition. There is definitely a split between viewers as to which franchises they like better, but Marvel Studios just knocks it out of the park when it comes to revenue.
Both studios, in my opinion, produce two very different yet satisfying superhero experiences but there will always be people who add fuel to the inevitable fan-boy fire. What do you think?