Every browser reimplements the native platform widgets. Even Safari! You have to, because the native platform widgets never support all the features a browser needs (CSS styling, JS event interception, etc etc).
Unfortunately, copying the look and feel of the native platform is an endless treadmill as those platforms evolve, and for obvious reasons Safari is always going to be better at keeping up with that on Mac than Firefox is.
Dude, I know - read my original comment, I'm clearly aware that Chrome had to implement their side of things.
Firefox goes out of their way to draw controls that don't fit in. Chrome, for all their faults, tries very hard to emulate the proper look/feel/functionality.
AFAIK Firefox does not "go out of their way to draw controls that don't fit in". On Mac and other platforms, the policy is that the controls look and feel like their native counterparts (unless overidden by Web authors) ... unless it's changed since I left Mozilla, and I don't think it has. In some cases, however, that has not been achieved. I haven't had a Mac for long time so I can't speak to the details of what works and what doesn't.
FWIW I use Linux and on Linux, Chrome makes no attempt at all to use the native platform theme, while Firefox does a pretty good job.
I will, however, apologize for saying they "go out of their way". I fired that bit of text off without thinking, but it's needlessly assuming (and likely outright wrong) on my part. Thanks for the correction.
On Windows and Linux, Firefox draws native-like (win32 or gtk) controls. On Windows (possibly Linux), Chrome draws custom controls (for <button>, sliders, and right-click menus).
Unfortunately, copying the look and feel of the native platform is an endless treadmill as those platforms evolve, and for obvious reasons Safari is always going to be better at keeping up with that on Mac than Firefox is.