Of course you can compete on an instrument , you can compete in range or a bunch of ridiculous things, How the heck do you compete musically assuming technique/skill/talent is present. if I ask you whose your favorite musician on the trumpet you should say who ever the best is, because why wouldn't you like the best right? Why is your best not my best; whose best is the real best musician(not trumpet player)? It doesn't work that way cause we all are attracted to the soul of the artist we can relate to which cant be rated or scaled by some arbitrary tool.
If your referring to internal competition then this was a big misunderstanding because competition usually entails the presence of other people . Motivation and competition are also to different things, i can hear a musician and think damn I wanna play like that I'm not competing with him, I may not even exist to him h/her how can I compete with them? O dear ! Diction!