The Institute is the best faction ever.
On PC, you can mod any pattern you want, so I'm impartial when it comes to paint job, but I guess I like the BoS. I like the BoS symbol and I like the general color, but the Institute exclusive paint make the Power Armor look very high tech and futuristic.
Vanilla, the Institute X-01 is probably the sharpest. It's certainly the best as it can actually be applied to X-01 armor.
Once mods are available to consoles that might change though, as there are mods that allow any faction paint to be applied to any type of power armor. I use the blue version of http://www.nexusmods.com/fallout4/mods/3176/? Minuteman power armor paint mod, and think it looks pretty sharp.