Welcome to Utah! I frequent both establishments quite often. They are within a city block of each other so you could probably hit both. I think that the food is better at Redrock and the Beer is better at Squatters. Squatters also has a much bigger selection and some special releases available right now. If you are into sour beers I highly suggest their 529 Oud Bruin. They also have a Farmhouse ale that is really tasty.
Another suggestion is the Bayou its not a Brewpub but has a huge selection of beers (257 bottles and 31 on tap) and the food is awesome.
http://www.utahbayou.com/Also if you want to take some beer for the road a new brewery just opened up a couple of months ago a few blocks from Redrock and Squatters called "Epic Brewing Co". They are a bottle shop only. The have made some excellent beers Copper Cone is one of my new personal favorite beers in Utah.
http://www.epicbrewing.com/
On Tap: Bird Of Prey IPA(all Falconers Flight), Lavendar Saison,Oak Aged Tripel, Espresso Oatmeal Stout
In Fermentor: Berliner Weiss
In Oak Barrel: Oud Bruin
Up Next: Porter,DIPA,Imperial Porter
Corporal Latter Day Saints Division UT 