I have not read through Princes yet.
My experience so far with HoTDQ (currently up to chapter 4) as a player is a mix of meh and frustration. Story line it's OK, we have "bought in" to the whole AP idea, but from an adventure design point of view there are sessions where I really come away feeling frustrating.
It's absurdly high DCs attached to ambushes, railroady fight (Cyanwrath), poorly written encounters (deadly * 3), and being pushed and rushed around from A to B without really time to strategize, recoup, or even really get to know our characters. The rewards are also very poor, we're quite often left wondering why bother even adventuring at all when you only manage to scrape together a couple of coppers after being badly bruised and beaten.
My character is basically getting so frustrated that he is on the path to evil, torturing those he captures and taking it out on them.
Your group might not care, but I know I'm getting frustrated with the fact that many parts of this module from a mechanical stand point do not match the abilities of our characters. Some things are just way too hard, and we're constantly getting our butts kicked for very little reward.
It's not the writers fault since they were creating this module without much guidance from the rules, although they do seem to like to put the players in near impossible situations from time to time. On the other hand, you can probably avoid a lot of these scenarios, but you also miss out on a lot.
Now, I'll be picking up PoTA soon, so I'll be able to have a read through it and compare. I'm making the assumption though that it's a bit more polished rules wise.