What do you want to do with the rifle? Both are very good rifles with pros and cons.
The FNH uses the pre-64 type Winchester 70 action and as I understand it, the same action as the FNH SPR. My main precision rifle competition rifle is a 6.5 CM custom built off of the FN SPR action and I love the action. It is smooth, rock solid reliable, has a 3 position safety that locks the firing pin when on safe, and has an excellent factory trigger that is easily adjustable. The TSR XP has a good magazine system, but FN mags are not as common as the AICS magazines that the Ruger Precision rifle uses.
The Ruger has a lot going for it also. It is modular so you can easily change the stock, hand guard, and other parts. It's become very popular at an excellent price point and there are many aftermarket parts available including prefit match grade barrels. The Rugers that I've seen run in our club competitions work very well although I've seen them have some feed issues when used with Magpul magazines. Those running AI AICS magazines tend to be very reliable.
Perhaps what will determine your decision are the calibers. The 308 is still in very wide use and match grade factory ammo is easily available. However for precision rifle shooting, anything the 308 can do, the 6.5 Creedmoor can do better. Factory ammo is also easily available. Recoil of the 6.5 CM to me seems like its halfway between the 223 and the 308, spotting hits and misses is easier because the rifle doesn't move as much under recoil, and shot to shot transitions are faster. Wind drift and bullet drop for the 6.5 CM is roughly 40% less than the typical 308 ammo, giving you that much more margin for error on your wind call. If it were me, even though I love the FN action, I'd get the Ruger RPR because it's in 6.5 Creedmoor