I don’t really get the comparison between the two. Babel, yes, is a transpiler. Typescript is a (superset) language. And yes you will need a Typescript capable transpiler to be able to run it in the browser.
Using ES6 is a no brainer, it’s the new version of Javascript and soon you will not need a transpiler like Babel to run it anymore. It just runs in the browser. The only question remaining is if you want to ADD Typescript to that. You see, when you use Typescript, you automatically also already use ES6. It’s not a one versus the other.
Yes static typing is cool and useful, but it’s not the answer to everything. You still only check types compile time, it’s just a feature that you also have to accept is not built into the core of Javascript. I think good coding practices, TDD and a good architecture are way more important then static typing.
Another thing not to like about Typescript is that you will always need a transpiler. Without Typescript and using HTTP2 in the coming years you will be able to deploy the code you write and just run it immediately. Also your developers can learn good Javascript coding practices instead of using Typescript.
I’m not saying Typescript is bad or that you should not use it. Just remember that in the and it is nothing more than syntactic sugar over Javascript and it will never add any actual language features.