Haven't looked at Babel's, but the output from Typescript is human readable and not much bigger than the original. The more polyfills (lower your target lib aka ES3 vs ES2015) The bigger the output.

Even targeting the oldest crappiest browsers doesn't add that much. Some maybe 50kb for polyfills injected and code bloat of 30% ish. Not much price to pay to use the latest features without caring about compatibility