Firefox developers did a lot of work in the recent years to reduce memory use and leaks (MemShrink) and visual stutter (jank), and e10s will improve the latter even further (while regressing memory use a bit).
However, Firefox will not magically better itself; developers - paid and volunteer - will need to fix issues as they are discovered, and that means that if you run into performance problems, you should file a good bug.
I use both Chrome and Firefox on my Windows 7 box, simultaneously for various reasons.
The Chrome (vanilla install except for uBlock Origin) performance is... not great for me, at least once I get more than 10-15 tabs open, mostly when switching and/or opening tabs. A lot of it seems to be swap-thrashing.
Firefox performance on the other hand is OK to great, even tho it being my main browser with usually 50+ tabs open (with tons of overlap with those Chrome tabs) and rather add-on laden. I am using Nightly since forever, with e10s off at the moment because of one or two add-ons that would fail otherwise; tho I also have Firefox Stable installed and when I use that it behaves the same.
Sure, webgl and/or js benchmarks might be a little behind on Firefox (tho not by a large margin). So that nifty html5/webgl 3D ego shooter might perform a little worse, but that is nothing I personally really care about. Firefox excels for me for regular browsing performance, and that is what I want.
Chrome on OSX always performed abysmal for some reason, so I am using Firefox (Nightly) exclusively on a recent MacBook Pro, which runs fine (sans the occasional memory swap/uncompress stutter when switching back to really old tab that got paged out).
I cannot comment much about startup performance as I usually have long-running sessions in the order of days or weeks, but it seems OK for both browsers.