It's very, very subtle, and it doesn't really matter.
The honest reason that they're both there is that Make Movie came first, before there was a render queue, and we just haven't gotten around to eliminating the redundancy.
The subtle difference that persists is that the first time that you choose the Make Movie command, it will prompt you for an output name for your file, so you don't have to click to set this in the Render Queue panel.
Also, "Add to Render Queue" can add multiple selected Comps in the project panel, besides the currently active Comp in the Comp panel.
"Make Movie" only adds one at a time and it's only available if there's an active Comp, right?
Yes, Adolfo's right. I was focusing on the direction of "but why would I ever choose Make Movie?" In my opinion, you might as well forget that Make Movie is even there. As Adolfo has pointed out, there are some things that work better when you use Add To Render Queue.