Same. It is like matching brackets. Two sentence ends, one quoted and one quoting, so two full-stops. And like putting exclamation/question/interrobang/other marks in the right place depending on who is using them (quoter, quotee, or both).

Of course you can shorten your quote by one character and leave out the inner stop, and I'd say that was equally valid. I would tend to do that unless I want to make it absolutely clear that what I was quoting wasn't a run-on sentence that continued after that point.