I just installed Gallery 2 on my site yesterday and I'm still playing around with it (which theme are you using, Tony?). I'm in agreement that it's far better than Gallery 1. One thing I'd add to Tony's post is that Gallery 2 also lets you upload images from Picasa.

The major downside I see to Picasaweb is a lack of integration with your site. You're always going to be stuck with Google-white.