I am replying to this thread as someone who has beem using Chromium for the past several months, switching away from Firefox because of the huge memory footprint. I've seen it consume about 2GB of memory easily, and then it would become sluggish. Things would not respond fast, and it would hang for several seconds every 20 seconds or so. It had to be killed a few times per day.
Chromium is more resistant to that. Each tab opens a separate process, and manages its memory better. However, Chromium lacks excelent add-ons (from a webdev perspective). No decent Firebug (Firebug Lite isn't very good), and some other add-ons that are not as good as the Firefox counterpart.
Yesterday, I decided to have a try at the newest Firefox, and so far, I'm pretty much pleased by what I see. I got the Nightly, to stay at the bleeding edge. Browser is open since yesterday, and I haven't seen it consume over 500MB of memory, which is definitely some improvement. I don't think the JS engine or rendering is as fast or responsive as Chromium, but I can live with this.
I have used nightly builds from Firefox a long time ago, and although we know it can seriously break, I still haven't seen this happen (and I updated almost daily).
I'm back to Firefox (err... Nightly is the codename now), and happy. If someone thinks memory management from this Firefox 7 isn't too good, give a try on Nightly, you might be as surprised as I was.