I have ridden & shown both english & western though now I ride 95% western. I think tinyliny's list was excellent. Just wanted to add that for me doing both for lots of years I found it benefited me greatly as a rider. There are things from both styles to pull from and make you a better rider overall.
Don't hesitate because it isn't the cool thing to do or they might think you a snob. Tell them you just wanted to try it out and broaden your horse horizons