10 companies are responsible for 57% of the changes to Linux. This is better than the typical 1 company responsible for the majority of changes in a browser, but it's not remotely close to "hundreds and hundreds of independently working engineers". Volunteers only make up ~8% of the changes.

What we don't have is any browser that's a multi-company project, though. WebKit used to almost be that, but then the blink fork happened. The closest currently would I suppose be Chromium as it's also backed by Opera.