Going by Wiggle the Tiagra 11-34 is 350g and the XT 11-34 is 323g so very little in it weight wise.
I have a bike with Tiagra 4700 and swapped the OE 11-32 for a Tiagra 11-34, when it was brand new, without changing the chain. Shifts perfectly and the cage looks normal even when going big to big which you shouldn’t ride in.