Asking what airbrush people like to use is like asking which is the best -- blonde, brunette, redhead, etc.
Personally, I've used paasche, badger, iwata and other off brand brushes extensively. I prefer Iwata at this point, as they are the most durable, reliable and consistently performing brushes I've ever used.
But that's a matter of opinion; other people will argue until the cows come home that brushes made by badger and Paasche are in the same league. They have brushes that are similar, i.e. similar design. The new talon and the renegade brushes are similar to the design that you'll see with the Iwata brushes.
I've never had an Iwata brush fail, but I've had other brushes from other companies fail entirely. I'll never use them now, unless I have a good reason to. For instance, I like my SAEM Paasche H to lay down priming coats and spray decanted paint.
It also depends on what you would like to do. I can do extremely tight work with many of the Iwata brushes, but woudl be very hard pressed to replicate this in the same manner with other companies brushes, without using masking or some other shield.
Keep in mind, the airbrush is only one part of your setup. You need a good, reliable air source and have good control over your media (know how to thin, mix and otherwise control the nature of your paint.)
Additionally, any good airbrush artist will demonstrate that the airbrush is only one tool for you to use. You'll continue to use pen/ink, paint brushes, etc., so a mix of media as well as different techniques will give you the best results. You can do a lot with an airbrush, but some things are just not that efficient to do with that tool.