Where does the difference in TV connectivity lie?

If one were to connect an Xbox360 or PS3 to an HDTV with an RCA connection, rather than DMI or HDMI, where would the difference be seen?

Would the resolution only be 640X480, or would it still be 720/1080? Would textures seem less sharp and colours less defined, or would the difference be minimal?

Same question for playing next-gen on a SDTV, where is the difference noticeable? I mean, models are still built with the same polygon count, and bump-mapping is still there, so where would you see the difference?

Finally, for those too poor to afford an HDTV, would a $75 VGA adapter be a good option for playing a next-gen console through a PC LCD monitor in comparable quality to an HDTV? Or would HDTV be worlds better? (Also, would the monitor need to be widescreen or could a standard shape monitor still display games properly?)

In all cases it is the lowest common factor that's important, the original polygon count is irrelevant. Once you've gone to a lower standard the information needed to go back to a higher standard has been lost.

The RCA connector is intended for output to SD devices, so you will only get SD quality images, near enough 640x480. Obviously the same applies on an SDTV.

Using a VGA type connector on a system with such an output built in (or an internal add-on) you should set the output to match the natural resolution of the monitor, that's the best quality you can hope for. If performance restrictions mean that you can't set it high enough then you will get pixel cropping but it should still be much better than SDTV.

If you use an external VGA converter then the best output it can give is dependant on the source; if that's the RCA connector then you will still only get SD quality at best, and possibly not even that.