My feeling is to wait them out if you can, and let the algorithm do its thing. If the competition's link profile is the way you describe it, then how long will the site last at the top of rankings? Not long, I would think. Time and time again, we see ranking spikes from low-quality links followed by monumental crashes. I even remember reading a study about this -- how algorithmic penalties are often preceded by impressive spikes in rankings.
In spite of the fact that we know these legacy forms of link building are dead, people are still doing them with gusto -- particularly offshore SEO practitioners, who are happy to make short-term money on short-term results. My guess is that your competitor knows little about SEO, read something about how important it is to have lots of links, and went out and hired the absolute cheapest SEO'er they could find, without having a clue about the business. I would imagine he has a big smile on his face right now, and he's telling people, "it's so easy to rank #1 on Google! All you have to do is pay someone a little bit of money to build a lot of links!"
I'm highly doubtful, however, that he'll remain in that spot.