I've read a lot of positive insights in using CrossRider compared to its competitors but I haven't read anything related to any of its limitations (functions, speed, integration with third party services, etc.).
The biggest drawback of using any framework is the fact that you are bound to the limitation of that framework.
However, if you see that what you are looking to achieve is feasible using the framework (and most likely Crossrider will fit your needs) then you will find out that it is going to save you a tremendous amount of time and effort, in comparison of doing all the hard work yourself.
I would suggest that you will check their cross-browser development framework and see what can be done and can't be done. And if what you are looking for can be done - obviously go for it. Instead of learning the Firefox and Chrome APIs along with C++ for IE development, you only need to be familiar with Javascript (and jQuery).
Crossrider has an online IDE which lets you dive right into the code in matter of seconds. No need to download any development SDKs (unless you really want to), and you will see your code changes take affect in real-time.
Other benefits that are worth mentioning are their publishing tools, such as direct download links, the widget generator and the dynamic Window installer that can install your extension on all browsers automatically.
(disclosure: I am one of the employees of Crossrider)