SakaSteph said it all! I've run a couple of fanfic awards and participated in a lot more as a nominee, and of them all, the Felix Awards are definitely the best! What I like about them most is that they're fair and reliable, something a lot of the old awards were not. I was nominated in quite a few that never followed through on announcing winners, which was lame. I was also nominated in some where the only people who won awards were the owner's friends. Hm, suspicious much? LOL
All that aside, I do like the idea of fanfic awards. I think they're a nice way to spotlight and celebrate quality writers and stories. It's not like we write for money or fame, so to have some way of recognizing each other for our efforts, even if it's just with a title and a graphic, is really nice. I love how the Felix Awards have become like a major event, like the Oscars/Grammys/Emmys. I really do look forward to the night the winners are announced and what creative way they're going to be presented!
As far as how meaningful they are... at the end of the day, it's really just a title and graphic, based on someone's opinion - either a handful of voters or a judge - and so it's not something to brag about or get all bent out of shape about, but I'm not gonna lie, there's still a nice sense of satisfaction in writing a story that wins that title and graphic! Like Steph said, I think judged awards are more meaningful, assuming there's some sort of criteria used in judging and not just a random judge's opinion. When there's voting, it's really just a popularity contest - but it's still fun to win those and know that a lot of people like your story. It's the difference between the Oscars and the MTV Movie Awards - the winners may be different, but they're all grateful just to be given an award. The best movies are the ones who can win at both, meaning they're critically acclaimed AND actually entertaining, and the same can be said for stories. That's why my favorite awards are ones that use a combination of judging and voting.