Browsers are pretty complicated, yes. Things like low-latency high-performance VMs, hardware-accelerated video pipelines, plus the details, like actual HTML parsing, CSS layout, a network stack, and so forth. Also, what matters is not just the complication but how fast you're trying to change things, and people are adding new things (flexbox, more complicated CSS layout modes, mode DOM APIs, etc) faster than ever before.
But also, in addition to a browser Mozilla is working on FirefoxOS, which involves a whole separate bunch of developers, since it's not like the browser developers are writing things like the dialer app for FirefoxOS. Also, you need QA, not just developers.
And yes, Mozilla has 1000-ish employees, for what it's worth.
It's not just Mozilla. If I look at https://www.openhub.net/p/chro... I see on the order of 600 committers with commits in the last month. And that's not even counting whoever is working on the non-open-source parts of Chrome. And not counting, again, QA and so forth.
And the worst part is, this is not a new development. Microsoft had over 1000 people working on IE6 in 1999, according to http://ericsink.com/Browser_Wa...
So yes, browsers, complicated.