I have all 3 systems. In my experience, there is a pretty noticable difference when going from 5.1 to 6.1. The difference is not as noticable between the 6.1 and the 7.1 systems, since in a 7.1 system both of the rear surround speakers produce the same mono signal that the single rear surround speaker in the 6.1 produces.
To answer your specific question, when watching movies you can get the rear surround speakers into the act if your receiver will decode dts-ES or DVD-EX movies, both of which are encoded in 6.1. You can also get the receiver to "matrix" a 6.1 soundfield by chosing "Neo: 6" (I think there may be 2 "Neo: 6" modes, one for music and one for movies, but I'm not sure). As I recall, the "Neo: 6" mode will also create a matrixed 6.1 soundfield from other audio feeds, but as for which type I can't be of much help as I haven't visited the vacation home in which the Onkyo system is installed for about 6 months.
When playing 5.1 movies, the rear surround speaker(s) are mute. I must admit that with a well recorded 6.1 soundfield ("The Haunting" comes to mind, but I've also heard good things about "Lord of The Rings"), the output from the rear surround(s) is quite noticable. In "Castaway", when the airplane crashes and Tom Hanks manages to get into the life raft and is being tossed about on those huge swells, I must admit to getting a bit seasick when listening in 6.1. That's pretty realistic, if you ask me. The effect does not present itself in 5.1.
As for TV sound in surround, there are a few "soundfields" in most receivers--the Onkyo TX-SR600 in front of which I'm sitting right now has "PLII Music", "Neo: 6 Cinema", "Neo: 6 Music", and "PLII Movie" in the "Surround" menu. It has "Studio Mix", "TV Logic", "All Channel Stereo", "Orchestra", and "Unplugged" soundfields in the Digital Sound Processor menu. I have a Denon that has "Stadium"--for a thoroughly disgusting experience, try listening to a football game, in which you already get a delayed sound signal from the stadium speakers, through "Stadium", which adds even another layer of reverb. It's undecipherable. So, to answer your question, it depends on how well you pick your soundfield how the TV sound will please you. Just experiment a bit and you'll figure out which ones to avoid and which seem to be usable. I seem to use "Studio Mix", "Unplugged", and "PLII Music" modes the most. Various modes use the center speaker more or less than others, so to figure out which you like just play with them a bit.