I've stayed precisely once at the Sheraton LHR (that makes me an expert). Checked in early (8 am) and was given a very miserable room (dingy, moldy, worn out and about equal to a motel 6). Called the desk to comment on the state of the room, they automatically moved me to a "removated" room -- same size, but an order of magnitude nicer. Freshly decorated, with much better furnishings, linen, etc. By no means luxurious, but comfortable. So the secret is to insist on getting a renovated room. Otherwise it is almost as good as the Skyline (but I think I will stay in London and not at LHR in the future, it still takes 30+ minutes to get from LHR to this hotel despite it being across the street from the future T5).