Stayed here for one night and at the Hilton for one night. My thoughts:
Hampton is new, and that shows. The lobby and rooms are very clean, and check in was efficient and without incident. The free breakfast is a nice touch (even for those without status), but does make the buffet a bit of a free for all in the morning.
Now the downsides. It's further from the airport than you think, and if you're driving it's not overly easy to find. Then there's the size of the rooms, which whilst ok for one person I reckon if I'd been with my wife we'd have been falling over each other. The whole room felt a little claustrophobic. It's also a trek back to the airport to get the train into the city; even with the free shuttle.
The airport Hilton was around €100 more expensive, but (I'm Hilton Diamond so other opinions may vary greatly if you don't have status) the better breakfast, proximity to the intercity train into Amsterdam, and the exec lounge offering a range of drinks and snacks makes that a price worth paying. Even though the hotel feels very dated now they're building the new Hilton next door and therefore not doing a great amount of upkeep on the existing property.
All in all, I'll likely stick with the airport Hilton in future. Nothing against the Hampton, but the convenience offered deserves the price premium, IMHO.