Barring browser/extension bug, browsers free up resources when they are no longer needed; Firefox clears compartments, Chrome kills processes and associated storage.
Firefox does its best but may take some time to clear the memory and may create zombie compartments on occasion:
Compartments are destroyed when they are garbage collected. This happens some time after the last reference to them disappears. This means there can be a delay between a page being closed and its compartments disappearing...
Sometimes, due to bugs in Firefox, the Add-on SDK and/or add-ons, compartments are created that are never destroyed. These are a particular kind of memory leak, and they cause Firefox's memory usage to increase gradually over time, slowing it down and making it more likely to crash.
Chrome uses a process per tab (and really subprocesses for some entities within a tab as well IIRC e.g. plugins, iframes, etc.) to the same effect. Though a quick check against chrome://memory-redirect/
and refreshing a tab looks like the same pid
is used. So a refresh is not a completely clean slate.
FWIW Chrome has a "Force Reload" that clears the cache and might be either useful for clearing more memory or a placebo: cmd-shift-r
I'm not really familiar with the internals but I've only seen things not reliably freed up between refreshes when a particular browser is getting too clever and trying to preserve things when you're not changing origins etc. in an effort to boost load performance.
In short, you could be tripping up a browser bug if you're not seeing memory freed as you expect but you'd want to use the various "about:memory" tools to verify that and at that point it would be on you to avoid such behavior and/or report the issue to the browser's dev team.
Otherwise, I think you're best served by addressing your own memory leaks within the page using the various tools available.