So if I'm understanding you correctly, the cash price of a United flight is
$338. Let's just go with that number.
If you're looking at this flight from the Chase UR portal, and you have UR points, the amount of UR points it'll cost will depend on which card you're logged into the portal with and which card you use to redeem your UR. That's because the CIP and CSP give you a 25% bonus (or 1.25x multiplier) on the value of your UR points, and the CSR gives you a 50% bonus (or 1.5x multiplier).
So a flight that costs $338 in cash will cost you:
$338/0.015 =
~22,533 UR on the CSR
or
$338/0.0125 =
27,040 UR on the CIP or CSP
UR points transfer to United miles 1:1. So if this same flight costs 37,000 United miles as an award seat, you'll need to transfer
37,000 UR to United to book the same flight that you could book on the Chase portal for as little as 22,533 UR. So obviously
in the case, booking through the Chase portal wins.
But one more thing, because booking on the Chase portal acts like paying cash through a OTA (online
travel agent), your United ticket purchased with UR points will earn you award miles on United. If you transferred UR to United, then used the United miles to book the flight, it would be considered an award flight that doesn't earn any miles. I know we're probably talking about a relatively small amount of miles here, but every little bit counts.
And one final thing, booking with UR gets you the travel protections of the card you're redeeming from.