No I dont know if chess.com shows the statistics somewhere. Especially since I dont have a diamond account.
I only know that 10|0 is the most popular.
And I think 3|0, 5|5 and 15|10 are also quite popular ? But I'm not sure.
Define "competitive" ? The faster the time control, the less time you have to think. It really isnt less or more competitive though, just different.
Obviously the shorter the time control, the faster you can play games.
As a general rule, the shorter the time limit for a particular category (blitz, rapid, classical) is the more popular it is and the longer the time limit the less popular it is. So for example according to this 10|0 is the most popular rapid, which is indeed the case. I could be wrong but I think something funny happened a few years back, that 10|0 used to be the longest blitz but was moved to rapid, and suddenly went from hardly being played to the most popular time limit.
It kind of says something a bit depressing about human psychology that players want to get the merit of playing in a longer time limit but end up flocking to the lower time limits of it. Personally I just play 3|2, though I have played 5|2 also. Having no increment is ridiculous if you ask me.
Is there any way to check it/ anyone knows the answer?