I haven't followed either's career particularly closely but I like a lot of stuff from both artists. The Imperial March from Star Wars and the dancing scene from MI:2 "Nyah" are some of my favorite songs from movies.

I don't know much about Zimmer from beyond his Wikipedia page but I did find this quote (from Wikipedia) regarding his stance on crediting the other musicians who help with the collaborative nature of modern production.

Originally I had this idea that it should be possible to create some kind of community around this kind of work, and I think by muddying the titles – not having "you are the composer, you are the arranger, you are the orchestrator" – it just sort of helped us to work more collaboratively. It wasn't that important to me that I had "score by Hans Zimmer" and took sole credit on these things. It's like Gladiator: I gave Lisa Gerrard the co-credit because, even though she didn't write the main theme, her presence and contributions were very influential. She was more than just a soloist, and this is why I have such a problem with specific credits.

Does he say one thing and act another way behind the scenes?