If you write type annotations in Flow, they're stripped away.
There's no difference. TS has some additional features which are purely optional that don't get purely stripped out, but you're not mandated to use them.
In my eyes, it's a philosophical difference between the two, Flow can be more easily integrated into an existing codebase by just adding //@flow at the top the file and has no features which can affect runtime code. Whereas TypeScript tries to be a different language altogether that uses a new file extension, adds new features, and has its own compiler.
When you can implement a tool like this using TS, let me know https://github.com/flowtype/flow-remove-types
Enums are a fair point, those aren't in the ES specs (though I suspect at some point they will be). However, they're an incredible addition and they really are just syntactic sugar for a more complex type of object.
BTW, typescript supports jsdoc-style annotations, and --allowjs even lets it typecheck javascript code. It also supports more, because nobody actually only wants those things; they're not that great on their own.
You might not think the differences is a big deal, but affecting runtime code is a pretty major line to cross. Not that there is anything inherently wrong with that, but at that point it becomes a different tool, in my opinion.
enums are a tiny, extremely useful and extremely optional part of the language and they don't warrant this label of "philosophical difference", IMO.