My WebAPI was deployed in the Intranet environment. That means security was not my concern.
It seems that CORS is much more friendly to the client and easier to implement.
Any other concerns I might have missed?
This is a pretty broad question, and could warrant a wiki unto itself. There is also quite a bit on google regarding the two, but I think I can hit a few key points.
If neither of these are a concern, I would just go with whatever is easiest or most familiar to you. If its a tossup, try CORS, since it is the more "modern" solution and JSONP is more of a hack, turning data into scripts to bypass cross-domain restrictions. CORS does however, typically require more server-side configuration.
If you're using jQuery, I'm not sure where you're coming up with the idea that CORS is "much more friendly to the client and easier to implement." See https://gist.github.com/3131951 . jQuery abstracts the details of JsonP, and CORS can actually be somewhat tricky to implment on your server-side depending on what technology you're using.
I recently developed a web app, using jquery and backbone.js, which reads from various cross-domain web services that we control, and ended up using Json-P instead of CORS because we need to support IE7 and it was a bit simpler on the server side (we run Django w/ DjangoRestFramework), and virtually the same with jquery on the client side.