Normally the 2 are separate for me.
Most bands i play in i don't usually listen to the songs except to learn them. Once i start learning the songs i tend to get more interested in the bands other work. There are some bands i just like to get a feel for how the bassist thinks and plays to help me replicate his style live.
In a nutshell the band i'm in at any one time will influence what i listen to for a bit.
On the other hand my own personal choice is so varied with a lean towards Prog.
Dave