First, yes, if you are staying at PBR you can hop over and use the pools at the other onsite hotels.
Second, both have slides (though PBR has more than one pool, I do believe only the largest, main pool as a slide.)
Third, as for which is better, that depends on personal tastes. There is definitely a "theme" difference between the two. Personally, I've always considered PBR to be more "romantic" than the other on-site hotels, but its main pool is very family friendly. And yes, if you were to walk from PBR to the parks, you would first walk right by the HRH. So yes, HRH is closer, but if you use the water taxis the distance isn't enough to be much of a difference.
With kids your age, I'm not sure the theme difference between the two parks will really make much of a difference. Personally, I'd probably do as you were thinking and go with the cheapest of the hotels. My only caveat to that might be if you are looking at Club rooms. I much prefer the club lounge at PBR over the HRH. Also, PBR is a bit more spread-out as well given it was made to look like a Mediterranean village.