In reality, some people have noticed some issues to do with the way the App Store installs things that's causing trouble.
The safe way would be to uninstall Growl 1.2 using the uninstaller (available here: http://www.growl.info/downloads) and then install 1.3 from the App Store. This will not lose any of your settings, they should all stay intact :)
As for compatibility, there are some applications who's support of growl has broken between 1.2 and 1.3. Some, because they are using a really old version of the growl framework (the code that lets them support growl). Others for slightly different reasons. I expect the actively maintained apps will put out fixes in the not-too distant future. The majority, I would say, do still work just fine.
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Important point: Uninstall 1.2.2, THEN install 1.3.
If you install 1.3 and then uninstall 1.2.2, the first step will put 1.3 inside the 1.2.2 prefpane (a Mac App Store bug) and the second step will delete both of them.
So uninstall 1.2.2 first, before you install 1.3.