To build Ultimate Rewards between the two Chase cards is why I got CSP in the first place.
I found myself in a very similar dilemma when I was trying to figure out if I should use my Chase duo of cards to earn UR or if I should use my AmEx duo of cards to earn MR points. I have pretty much come to the conclusion that I'll use whichever card gives the most points back, regardless of the issuer. But for my wife's sake, I simplified it to just the AmEx cards because they pertain more to most of her spending. I always pay for dinner on the CSP so she would really never use the Chase duo. The gas, groceries, and travel are more of what she uses most often, so she carries the PRG as her card almost always.