Don't mind some people's comments, I guess since everyone is such an expert they forget this is in the beginners forum.
You will hear a lot of opinions on this topic and vtrookie is right, you'll find an answer anywhere. But I know how it feels to search 100 websites to get varying answers; which is why I joined this sight so I could ask questions and get real responses.
Anyhow, to your question... In my opinion, all grain is much more fun and gives you more control over the beer. I did about 9 extract batches with steeped grains, doing partial boils, and then made the move to all grain. It did take quite a bit of investment to get a good hot liquor tank and a mash tun together, but there are cheap and easy ways to move to all grain. As far as the quality of beers, people make amazing extract brews, so I won't say one tastes better than the other. But since you mash in all grain, that essentially gives you more control over the fermentable sugars, body, alcohol content, etc than extract. If you're just getting into brewing, start w extract and you can always add equipment here and there if and when you decide to move to all grain. Starting w extract will allow you to focus on the basics, get your fermentation process down.
Hope that was somewhat helpful. I tend to ramble on. Feel free to shoot any questions my way, I'm no expert but I've been having fun trying