I rotate my bows around, but usually stick with one for long enough to get used to it before I switch to another one. Anywhere from a few weeks to a few months on one bow before I switch to another one.
I relate to Nigel's experience, and think the reason we sometimes shoot better with new equipment must have something to do with increased concentration or focus when we try something new, as he says.
Right now, I'm kind of having the opposite experience. I'm trying to shoot a longbow with wood arrows, and I shoot it so much worse than my recurves with carbon arrows that it challenges me to learn to do better with it. It seems like the slightest little tweak in my release, or the slightest difference in my anchor or draw length throws the arrow off at least a foot at the target, where the same thing might throw my recurve with carbon arrows off by just a few inches. I feel like it's really causing me to have to focus on my form to get it as perfect as I can, which I hope will help me to shoot better in general, regardless of what bow and arrow combination I'm using.