Overall, Typekit is a slightly easier to use service. Both offer great fonts, decent pricing, and are technically sound. The primary reason a designer would use Cloud.typography is when he/she absolutely needs to use a H&FJ font in a design. Otherwise, the options lean toward Typekit.
Chris’ overview is very accurate. His conclusion that Typekit is better for 90% of the people is correct. But I take issue with the above statement, that one would only use H&FJ if they need to — that needs to be replaced with “if they want to”.
Then again I’m definitely biased.