UTF-16 will handle poop just fine. UTF-16 handles higher characters in a manner just like UTF-8. Pile-of-poo is encoded as D83D DCA9 in UTF-16, The same size as it is in UTF-8.
There may be a distinct size advantage for some asian cultures to using UTF-16 instead of UTF-8 as it will allow for encoding more of the glyphs without having to add more overhead bits. How much this saves in reality I'm not sure.
I wouldn't use UTF-16 unless having to work with a legacy system. A lot of software claiming to handle UTF-16 is broken and really only works with UCS-2. You have to worry about endianess and so on.
If you develop an application for the international market you should probably go with UTF-8 as well. Maybe if you develop only for the Asian market it's a bit different. But in my experience significant amounts of text usually come in some form of data or markup format (HTML, XML, JSON, etc.) and usually those markup formats are defined in the ASCII subset. So UTF-8 still wins. Just take a random page from the Japanese Wikipedia and encode it in UTF-8 and in UTF-16. You'll see that UTF-8 almost always wins.
The advantage of moving to one standard, plus the backwards compatibility for most of the internet will outweigh any small size advantage that UTF-16 will have on real file sizes for some countries / cultures.
A saving of ⅓ on a text file will barely be noticed in a world seemingly governed by Moore's law in nearly every future metric.
(also my bad for using UTF-16 where I meant 16-bit unicode character arrays :))
There may be a distinct size advantage for some asian cultures to using UTF-16 instead of UTF-8 as it will allow for encoding more of the glyphs without having to add more overhead bits. How much this saves in reality I'm not sure.