When I was still young enough that I regularly would go to my friends' to play Xbox games I would typically log into my account on their xbox either way so that my gameplay would still go towards my stats/unlocks/achievements etc. That, and on the xbox, online multiplayer wasn't free so often times you *had* to be logged in to play or to get full support (typically guests don't have voice chat). Finally, logging in let you play as you, with your gamer tag that you use and not just a (1) after your friend's name.
I'd imagine taking your profile with you would be the prevalent method of bringing a game over, rather than your whole console.
Then again, I am/was a fairly hardcore gamer, so maybe all of those reasons to sign in anyway don't apply to the rest of the market. Either way, it would be more convenient than lugging your console, though lugging a console isn't that big of a deal (2-3 cords to unplug, swap it in when you get there to their existing cords).