Both are quality rifles in my opinion.
The rubberised finish on the X-bolt’s stock feels nice (though I’ve heard of some durability problems and it feels a bit flexy for me), I prefer its tang safety, it has a proper short action for the .308 chambering, and the 60° (vs. Tikka’s 70°) bolt-handle lift is a small bonus.
The T3X is so widely recommended that it’s almost boring, but for good reason; you can’t beat the barrel, trigger and smoothness of the action for the money, there’s a huge variety of configurations available, plus they’re dead-nuts reliable and simple to service, even in the field — the firing pin assembly is pure genius. I’d say it has better scope mounting options, too.
I’d be happy with either one, but the superior trigger means a lot to me, so the T3X is the one I personally chose when deciding between the options out there. Possibly worth mentioning that Howa makes a good rifle around this budget too.