This can get a bit confusing, especially if you happen to have many tabs open from both sites. It also looks a bit silly in the site switcher menu:
All the per-site metas (and MSO, even before the MSO/MSE split) have favicons that are grayscale versions of the main site icons. Why not do the same for MSE?
Conveniently, michaelb958 already wrote a nice user script to do just that (and I extended it to apply to the menu too), so you can easily see for yourself how it would look. Or just see the screenshot below:
So here's my proposal: Let's make this gray icon the official MSE favicon.
Update: The meta.SE favicon has recently been changed to a simplified outline version of the SE logo:
I'm not sure how much I like the new logo (for one thing, it doesn't seem to match the dimensions of the main SE logo), but at least it's different, which was the main point of this request.