I don't think you should be too concerned about this. Both Easymock and Mockito can be configured to be 'strict' or 'nice' the only difference is that by default Easymock is strict wheras Mockito is nice.
As with all testing there's no hard and fast rule, you need to balance test confidence against maintainability. I typically find there are certain functional or technical areas that demand a high level of confidence for which I would use 'strict' mocks. For example we probably wouldn't want the debitAccount() method to be called more than once! However there are other cases in which the mock is really little more than a stub so we can test the real 'meat' of the code.
In the early days of Mockito's life API compatibility was a problem but more tools now support the framework. Powermock (a personal favorite) now has a mockito extension
