Extremely dependent on a number of factors, mostly hardware and configuration. I had a Thinkpad T480 and on a stock fedora install it definitely died faster than W10, but after setting up TLP and Powertop I squeezed ~2 more hours of use out of it than Windows could manage. Ditto for my framework 13, I get all day battery life on NixOS but when I’ve tested windows on it I lose a few hours immediately
Mostly LibreWolf, but I’ve been enjoying Zen Browser recently. It’s based on Firefox but with lots of cool extra functionality baked in. It is still in alpha though and I’ve experienced some bugs, including it crashing my whole system a couple of times, but it’s very promising