In the consumer world, HD is considered 720P, 1080i, or 1080P and up. There is no True HD resolution. Any one of those formats would be considered HD.
If it were just a matter of resolution, there are already displays at 4K resolution that dwarf 1080P. There will always be a next big thing. Like 3D. It's coming. Bluray probably next year. So who will have it first for TV.
If you are looking for 1080P, not many providers will give you what you're looking for yet. DirecTV is either 720P or 1080i, with some new feature I just noticed on their service offering movie purchases at 1080P resolution.
We are not talking Bluray here, so when you are dealing with highly compressed sources like cable and satellite, resolution is not THE most important factor when considering image quality. It's the amount and quality of compression applied to all their sources, HD and standard. Before it even gets to the providers, networks already modify and compress their sources, before yet another level of compression hits them.
I've seen 480P sources look better than HD 1080i before. It's all about the source, not just the resolution. A DirecTV channel, even in 1080P, still doesn't compare to a good Bluray, but it sure looks a lot better than most, if not all Cable providers. That's not a blanket statement, as cable varies by location, but it is probably an accurate generalization. It doesn't matter if the Cable provider is broadcasting in 4K resolution. If it is compressed beyond all recognition, it will still look like ass. DirecTV should look the same everywhere and generally is preferable for watching TV on large projection screens. I had Timewarner cable at my old rental and Universal HD looked like they wiped their butt a couple times before sending it my way. And that was just on my old 61" projection.
I'm actually not an authority on providers by any means, as I generally stick with DirecTV for my work, for other reasons besides generally solid image quality. I've seen all the various providers over the years from home to home which helped me develop the opinions I have on them, but things change from year to year so consider my opinion just that. However, the fact that source integrity takes precedence over general resolution should remain constant. All sources being perfect, 1080P is going to be better than 720P. In the world of TV service, there are far too many factors and horrible things they do to the images in the pursuit of more, more, more channels that effect the final image quality far more than the display resolution. It's all about how much bandwith the provider has available, what type of compression they use, and to what extent that needs to happen to get all their channels jammed in there.