Don't think there's a best. A lot has to do with what's available. Assymetric tread and uniform across the tread is what you want. Many tires are doing like a three pattern tread, no good for the scooter, cause the ride would change from left turn to right.
I've not tried a RF yet, but would next time for comparison, plus the added safety if I pick something up.
Damn unlikely a franchise dealer will mount it unless you tell him it's going on your trike. My local Indy mounted it no questions asked.
I noticed very little difference in handling, which surprised me. It does wallow around on roads that the tracks are sinking a bit.
I don't notice any significant difference in the twisties when aired up right. You won't scrape the pegs as easily tho.
I think it's great in the rain, and It's runs like a champ on the highway, in town, or the curves, no complaints.
I don't notice additional road noise, I'm only DS on the rear, and she's mounted on the only rim I have, so all the time.
I started at 40psi, upped it to 41, then settled on 42. She wallowed around if I dove into a corner at first. But at 42, it's minimal. Keep in mind, a RF doesn't need as much air, stiffer sidewalls. They run 4 ply, mine is 2 ply.
Google Darkside motorcycle on the web, good site for info there.
This is my first experience on the DS and was very apprehensive, but I had no choice due to my MC tire not showing up in time for a trip. I'd done previous research and was fairly comfortable, but still nervous. Damn glad I did it! Good luck!
Mike