Although I don't know and didn't meet with the OP, I was (from another thread) there at the same time, on the same floor.
I was also very impressed with the standard of the service; it feels much more like a full-service hotel than the US-based HGIs I have stayed in in the past.
As a diamond, I was also upgraded; I didn't even have to ask, although the view from my room (742) was not as good.
I think the DoubleTree feels more 'special', but that's probably irrelevant given the location. This is definitely more convenient for T5 (DoubleTree also has a reasonable bus service to T1/2/3, although no tube).
I would actively recommend *not* using the Hoppa - at £5 pp it's likely to cost more than an Uber for three people, and for one person, the Piccadilly line is only a five-minute walk away and likely to be quicker than the shuttle bus, as well as only costing £1.50. True cheapskates can even get a free local bus to any of the terminals from Hatton Cross.