"Tom's Hardware did another benchmark showdown, since several releases of both Firefox and Chrome came out since their last one. Did Mozilla clean up its act and listen to its users? The test results are listed here. Firefox 13.01 uses the least amount of RAM with 40 tabs opened, while Chrome uses the highest (surprisingly). Overall, Firefox scored medium for memory efficiency, which measures RAM released after tabs are closed. Also surprising: IE 9 is still king of the lowest RAM usage for just one tab. Bear in mind that these tests were benchmarked in Windows 7. Windows XP and Linux users will have different results, due to differences in memory management. It is too bad IE 10, which is almost finished, wasn't available to benchmark."
I've always thought that FF was the biggest hog of them all, eating RAM like it was jellybeans at easter. This might require an upgrade.