When selecting games to join there is usually some sort of status bar next the room. It normally changes colour, red for crap connection, yellow for ok, green for good. Or something similar.
Usually you can just tell. If people in an fps or cars in a racer are moving about erratically, appear and disapearing and just generally being odd you probably have connection issues, but then if its only a single person, it's probably problem at there end. People will usually tell you if you are lagging.
Usually in a game like PGR 3 I couldnt tell the difference between offline and online as far as playing went, it was always smooth, if that makes sense... but I havent been on live for a while to see what it's like.