I think it just depends on what's important to you. For us, convenience is the highest priority so we prefer HRH for this reason. We never have to use the water taxi while there. You can walk from PBH, but its a considerably longer walk which includes walking the whole length of HRH as well.
If atmosphere/beautiful grounds is most important to you, they both are very pretty, but PBH would win this one for me. The look and feel of the resort has a lot of attention to detail and you really feel like you're in Europe. HRH has the hard rock theme of course, but the décor and atmosphere is more generic by comparison.
The other difference that sticks out to me is that HRH is more laidback and casual feeling. The service is still top notch, but seeing bell staff and other staff in short sleeves with visible tattoos, talking to you like a buddy but in a respectful/good service type of way is a really unique dynamic. Makes us feel comfortable there, as opposed to typical resort where staff can sometimes seem like robots. PBH definitely has a more traditional luxury type of feel, if that is your preference. PBH also seems more family oriented, whereas HRH has always felt like more adults are around and the pool atmosphere seemed to be more adult oriented (still family friendly, of course).