i use a combination of the both of them because both programs ultimately have been created for two completely different purposes. i'm still waiting for adobe to combine the both, but i think they enjoy the idea of making money of basically two similar products.
I use photoshop, but I find it tedious at times. I do find it useful and you can get some useful information from the net about how to use it. I'll have to give illustrator a try.
photoshop is more popular than illustrator but each software has its own advantages and disadvantages so its for you to analyze which software to use according to your needs.