I don't believe this makes any difference at all. Any number of times I have seen multiple characters with dramatically different balance skills get tripped and then stand up simultaneously.
There is some difference here. If you fail your original Dexterity check against a trip effect, you then make a Balance check to see if you can get up midway through the trip. This does mean you get up after 2 seconds on the floor, not 4, so there is some merit to it.
The issue is, if you've
been tripped in the first place, most of the time your Balance skill isn't high enough for you to get up again - because it's also based on Dexterity, so if you have a Balance skill high enough to get up quicker, chances are you never got tripped in the first place.
(Unless you decide to design a build with terrible Dexterity and stellar Balance, but at that point you've essentially created a character whose single notable characteristic is that they are good at
standing up, and you have to ask if any of it is worth it.)
What you can do instead is pick up a source of Knockdown Immunity. This isn't 100% foolproof, as certain effects can bypass it (being hit by a boulder, the spell Command, quest-mandated Knockdown during scenery changes and the like), but it should make you immune to Trip attacks.
Here's a link to a list of effects that grant Knockdown Immunity:
Knockdown Immunity.