When talking about TypeScript, you should consider that TypeScript is - compared to CoffeeScript - really young, and its first release was back in 2012. Typescript is highly addicted to the (nobody can say precisely when) upcoming ECMA Script standard. TypeScript also offers support for classes and inheritance as CoffeeScript does, but in addition to that TypeScript adds support for Types and Generics to the client side. The TypeScript syntax looks a little bit like C# and makes it easy for .NET developers to move from the server-side coding to the client-side. Microsoft is not only providing packages to write TypeScript on Windows but based on Node.js you can also write and compile TypeScript from any platform supporting Node.js.
Regarding the question “Which language should I use? TypeScript or CoffeeScript?” I can’t tell you the right answer. I always say something like “It depends on your team. Just give your team a rough introduction into both languages and give them the chance to write some spikes using both.”