I have mixed feelings and we sometimes use both.
Backing track: We started using this early this year. The good: It gives good instructions about what's coming (guitar intro, solo, whatever). The bad: The sound guys turned up the backing part waaaay too much. We vid all of our first services on Sundays. I watched the vid and I heard almost nothing of the live band. My solos.....drowned out 100%. Literally could not hear my guitar whatsoever.
I do like the click track. However, for a very, very bluesey solo I'm doing Sunday (Surrender/Linconln Brewster), I have to turn it off. The solo purposely is not on the time and I could barely play it with the click track on.....so since it's the last song Sunday, I'll hit the mute on my aviom and be fine.
Whoever is running the click track also needs to be very on top of things. We had a piano lead in rehersal and he lost the click. The drummer takes care of the click track and kept tying to sync it. Did not work. I think in general, if someone loses it enough that they're going far off time, you need to be ready to bail and just shut it off.