What websites? I use Firefox as my daily driver on desktop and mobile, and I rarely run into problems. Like so infrequently that I don't even remember the last time.
Some websites display warnings even though everything works fine, like web.skype.com.
But that's the closest thing to doesn't work I've ever seen on Firefox.
I was curious of what their menu looked like as I have one by my work. Haven't checked it on desktop, but on Android, the menu items never get loaded. ($10-12 for an á la carte chicken sandwich from a fast casual place is a ripoff anyway)
Edit: It looks like it's the mobile site/formatting that is broken. Using desktop mode lets the menu items come onto screen. (Firefox 126.01 on a pixel8pro with Android 14) The same issue seems to also be present with chrome under my work account.
I still argue that they are present, as I had to with it doing taxes a couple months ago. (Just not going to give those sites away)
No problems loading that page on Firefox for Android or desktop for me. Are you using Firefox or a fork of Firefox? Do you have any extensions or about:config changes that may be affecting the page rendering?
There are some sites out there that won't work. ESC Configurator won't work in Firefox because it needs web serial to program an ESC connected over a serial port. That's the only site I use that I have to run in chrome. I'm sure there are more out there, but they are not very common.
I encourage those in this situation to do their small, small part in fighting for the future of the open web by only switching to Chrome when necessary.
Last I tried, I had serious issues using it on Comcast's billing pages and Quest Diagnostic's site, among others. The pages would not load at all until I went to Chrome.