I'd say you should bring whichever guitar you're most comfortable with playing on, but since you say that's evenly split between your Strat and LP, that's not a very helpful suggestion. You do bring up some good points for taking the Strat over the LP, though. As for playing through an unfamiliar amp, I know how you feel. I've tried it twice before, and it negatively affected my playing until I got used to the unfamiliar tone..