Usually PP is available for less than only 16 dollars cheaper than DLH. With that difference I'd take DLH I think, even though Ive stayed at PP a few times and enjoyed it. If you haven't done either and both are within range its probably worth doing DLH, the pool is a lot nicer and yes the hotel itself is quite a bit older, it feels very disney.
As you're a WDW vet I'll put it this way. To me, DLH feels like a really themed disney hotel, and the theme is Disney. There really isn't one like this at WDW but it'd be like an old deluxe with a disney theme. The rooms at PP are very comparable comfort and size wise, and they are newer, but the theme feels like a moderate theme to me. There are splashes of Disney here and there which are very enjoyable, mostly with a beach/california theme, but its not as immersive. The grounds at DLH are better as well, although that doesn't really matter considering they are so close to each other.
If you were in a different position, say having done both already, I'd suggest Paradise Pier, but being the first time at either I vote for PP.
A final note I really notice as a DLR vet but one who recently went to WDW a bunch of times over the past few years, there are no food options at the hotels like there are in Florida Disney hotels. Its quite annoying, there is no food court basically, just restaurants. The location of the Hotels, opposite side of Disney from all the other stores and hotels, means its a long walk to get food from a place like Denny's, Ihop or Mcdonalds at reasonable prices that are readily available at every hotel in Florida. Theres not much you can do but its something to be prepared for. Food courts aren't obviously the norm at hotels but they are in Flordia ones and I really dislike the lack of them after being exposed to it there.