There was a bug with our "Greaselion" component in versions prior to 1.0.41, which could cause some excessive resource consumption (usually for macOS users). We found and fixed it in 1.0.41, however. You can confirm that you're on this version via the brave://components page. Check for "Brave Local Data Updater", which should be up to date.
Performance on Linux is pretty nice - until I open more than a
handful of tabs, which then leads to the computer spending more
time swapping memory than anything else. Which is probably fine
for the majority of users, but kind of a dealbreaker for me. And
I don't plan on expanding memory just for the browser.