This is almost certainly caused by an extension. If you use Firefox with few or no extensions (e.g. 1Password doesn't cause problems) you'll find this doesn't happen.
Having said that, if someone is experiencing bad performance and they do have extensions enabled, temporarily disabling them is a good diagnostic step. If performance improves, it's clear that it's an extension at fault, and then bisection can be used to work out which one. Otherwise, it's clearly a Firefox problem and a bug report (bugzilla.mozilla.org) would be very helpful!
Chrome on the other side, starts degrading my entire system's performance forcing it to hit swap memory the second the string of tabs on my top bar threatens to stretch across the screen. No need to wait for 'months of use without closing'...