The difference is, chrome allocates what it needs upfront, and that's all it uses. Firefox keeps increasing its usage.
That means that when I want to leave a website open on my server for a month, I use chrome because I know exactly how much memory it's going to use. If it was firefox, at the end of the month even the swap would be filled.
The only way to free up the memory is to close firefox. Closing tabs doesn't do anything. I can 'killall firefox' and then reopen it to the same 50 tabs, and the memory usage after they're loaded again will be several GB lower.
I don't know if you count memory exhaustion as a 'crash' per se.
Does opening another program cause system instability? I don't know how you are monitoring it, but it sounds like Firefox is making use of the available ram for a cache. There's no real difference between cache and free memory, so using more is only a good thing.