I'm inferring from your post that you've been using the TI flats on your Fender P and you like them. If so, you like super-middy tone on your P, since the P is pretty middy to begin with and the TIs are very mid-forward. The question I have about your other P is whether you want a similar middy tone or something that contrasts. The Sunbeams are, if anything, a little mid-scooped and will give you a different basic tone before even considering the rounds vs. flats difference. Some people like slightly mid-scooped strings on a P so they kind of balance one another out, so if that's what you think you might want, Sunbeams are a good choice. If not, some more middy rounds might be better. TI jazz rounds, maybe, if you can afford them?