Chromium and Firefox both consume obscene amounts of memory just to do basic things, more or less equally. However that changes when you're working locally using many applications, compilers, several terminals, code editors, and many documentation tabs open in the browser (can't close all docs I need whilst coding)
I've stress tested the machines I use for work and forced the memory available down to a lower limit to see how these two browsers behave under different conditions. Chromium / Chrome doesn't relinquish RAM as efficiently as Firefox does. Firefox uses inordinate amounts of RAM, but it knows better when to free it, and I'm able to use even limited memory configurations under stress tests with many tabs open. Chromium / Chrome just freezes randomly if you have 8 or 10 tabs open whilst doing equivalent work, sometimes to the point of halting the whole system.
For heavy duty work, Firefox just works better.