It depends what the web content is.
Recently, I started getting "running out of memory" alerts from Windows if/when I have Firefox (Ghostery/Flashblock/Adblock) with a bunch of tabs open (strategy guides, mostly) with iTunes and SWTOR running. It's only happened a couple times (I have all that open now, no problem.)
I wonder if a recent version of Firefox has a memory leak, or if it only happens with certain web sites... *scowl*
Anyway, 16GB would probably hide the real problem. It's also cheap enough that I don't think a semi-serious gamer has an excuse not to put 16GB in a new build. I'll probably hobble along with 8GB for a while longer.
Chrome and Firefox are both firmly in the "will take as much RAM as you have" category of applications.