I usually play with my favorite Pokemon, although I try to find a balance between power and favorites. Most of my favorites actually have decent (and sometimes exceptional) base stats anyway, i.e. Hydreigon, Dragonite, Kingdra (gee, Dragons, go figure). Some are just kinda cool (to me anyway) such as Roserade, Luxray, Galvantula, Sceptile, Mightyena, Lucario, and Manectric.
I find that when I play with Pokemon I hate, I can't do nearly as well as if I had favorites.