That assumes that your competitor is ranking higher because
of those links, not in spite of
them. You could end up hurting
your site if you seek links from many lower-quality pages simply because your competitor has a link from those pages.
You should always use your common sense when evaluating links you find pointing to competitors' sites. Don't simply blindly copy their linking strategy thinking this will help you get ahead.
Beyond that, you need to think outside that box and seek links from other reputable pages that do not
link to your competitors. If all you do is copy
them, you'll never be able to exceed
their performance. All you'll do is continue to run second to them (because they got the links first
so their links will be older than yours -- you'll always be running second).
Mere copycats will not be winners in the long run.