I have tried long-term aged beers (year or more) side by side, one with o2-absorbing crowns, one without, and swear by the difference. While it seems you want some oxidation in a long-term-aged beer, they generally just have a much better flavor/less sherry-like with an o2-absorbing crown.
However, when judging at a competition recently, I had another judge tell me that one should not use these on hoppy beers, as they will absorb the aroma and leave you with a aromaless AIPA/IIPA/APA. Does this make any sense? I would think it would make even more sense to use them on hoppy beers since they oxidize so easily.