You're asking a question about apples and oranges. REST is pattern used in creating web services. I'm not an expert on it, but you can find plenty of details on Wikipedia. WCF is a Microsoft technology for creating web services (primarily using SOAP, although it's so configurable that you can do REST on it as well - see ASP.Net WebAPI).
Pros for WCF:
- Very configurable - If you can imagine it, WCF can probably do it.
- Simple to use if you're sticking to the Microsoft stack. Visual Studio does 90% of the work for you.
Cons for WCF:
- Very configurable - It can be a bit of a pain to get it do exactly what you want sometimes, especially if you're new to it.
- There can be some problems communicating between different technology stacks. I've heard of Java services curling up and dying when pointed at a WCF service. As far as I've heard, this is a problem with the Java libraries, not WCF, but who knows for sure.
That's all that comes to mind right now, but hopefully that gives a you a decent impression on WCF.
