The most salient difference is that the abbreviated version of rugby involves a much higher degree of variability. For example, the US team recently won the London 7's, beating England and Australia in their final 2 games (we would NEVER beat England or Australia in 15's with our current team, though I'm optimistic that we can at some point in my lifetime). You'll see this in 7's because a quick game can get out of hand after 2-3 tries by an enterprising opponent.

We (BYU) dominate in 15's because we have multiple levels of control. It would be a long discussion, but defensive tactics, offensive options, and superior athletes from #1-15 leave little opportunity for a lesser opponent to beat us.