I have stayed at the DLH 3 times and the PPH once. I love them both. I have two boys, aged 7yo and a newly-minted 4yo. Only DS4 and I stayed at PPH in February.
The rooms at the DLH are a bit larger, and have a bit of Disney theming. I expected the boys to enjoy the glow-in-the-dark pixiedust on the wall, but I was surprised when they noticed little details like the characters in the wallpaper, and the scenes on the quilts.
They absolutely love the pool area, with the big pirate ship and crocodile, not to mention the waterslide.
This last trip the boys played with the miniature Jungle Cruise boats in the center of the property (you pay about a dollar to radio-control a boat for a few minutes.) They loved that, too. And this trip DH took a stroll through the waterfall area for the first time, and thought it was lovely. He came to tell me all about it, and I reminded him that we'd seen it (a couple of times!) on our first trip in 2006. But I think on that trip he was more interested in getting to the park than enjoying the waterfall, so maybe that explains it.
I didn't see the pool area when we stayed at the PPH, but friends have said the kids would love that, too, because it has a big waterslide. We also had a DCA view from our room, really spectacular!
I think for your first trip, you should stay at DLH. There's lots to see and do. And on your next trip, stay at PPH. That way you can judge for yourself. You really can't go wrong either way!
ETA: In case this influences you at all, Goofy's Kitchen (character meal) is located at the DLH, and is the most popular character meal. The Lilo & Stitch breakfast (our 2nd favorite character meal) is located in a restaurant in the PPH lobby. If your kids would enjoy a character meal, these two are a lot of fun!