Before you blame it on the browser
I must say that FF7 is great when it comes to addons and security. I am running a Win7 x86 (32 bit), on a 2nd gen Ci3 with 3GB RAM.
The main reason why I don't like IE is because of it's inherent MS qualities. Chrome I don't like because its just not there yet; and it does crash repeatedly.
However; before we blame our browsers for RAM or CPU consumption, I have found that I have to control how all other applications including the OS itself connect to the internet. Now we all know that each OS is designed in a way to divide the network connection or band-width between browsing, downloading and system requirements. I have found that any browser will take more time to load (start) and will consume more RAM if I was already downloading OS (or other software) updates, and this is true for any browser..
Simple reason really is that the browser will be making a request for RAM & bandwidth which is already being occupied in part by the OS or other apps. The CPU will then have to hold that request in the background until it has allocated the needed resources and recalculated the load balancing to accommodate for each request.
Regardless of your H/W or S/W configuration and regardless of which browser you would like to use; you should not have crashes or notice any RAM spikes if you are SURE that nothing from the OS or other apps is connected to the internet in the background. I have had instances where I had more than 50 tabs opened simultaneously without trouble.
For me; IE is good but it is still MS and that's all kinds of bad. Chrome still needs a lot of work to be done. FF is the best around all-in-all.. But to tell you the absolute truth; I STILL MISS NETSCAPE!!!