All three pools have zero entry and sandy beaches. Hard Rock and Portofino have slides, while the RPH has a water station type thing with water guns, etc.
We just got back from 10 days at PBH with 7 kids in our party - 3 8 year olds, 2 10 year olds, 1 15 year old and 1 17 year old. We swam in both the PBH and rented cabanas at the HRH for a day. The kids preferred both pools over the RPR pool from previous stays, but that was because of the slides.
I do think they preferred the HRH hotel pool, but the PBH was not the least bit stuffy. And with 7 kids in tow, we would have experienced stuffy!

Lots of kids around and they got a kick out of all the pails and shovels laying around in the sand. The PBH's baby pool has a large Little Tykes type of pirate ship in it. The HRH baby pool is just a round circle.
My preference is the HRH pool because of the cabanas and the ability to get food after 6pm. We were swimming one evening at PBH and decided to just do a pizza poolside, but couldn't because the grill closed early. Really a pain with 7 hungry children.
So, we will continue to stay at the PBH for the luxury, but rent cabanas at the HRH for the ultimate swim day

And the walk from the PBH to the HRH was about 4 - 5 minutes - not at all bad even in the scorching heat of July.