Hi Peter.
This is a very common use case for Alfesco, a classical document management and indexing project. While executing some rules is an added value, it is easily done with Alfresco.
OCR is not included in Alfresco and probably should never be, since it is a science of its own. Most other ECM venders also use 3rd party systems or have acquired OCR/FEC companies.
From the two you mentioned, I guess Abbyy will be much cheaper for the same features. But, as I said, OCR is a science which depends on your requirements, your language, state of your forms, tolerance for mistakes (use case scenario), etc.
I do not know any details from your case, but my first hint would be Abbyy recognition server, which easily fits the mentioned scenario through Alfresco rules. You can even get by with super affordable Abbyy product that just listen on hot folders, which would in fact be Alfresco CMIS folders. There are many ways…
Keep in mind that most Abbyy components are Windows only, as is the case for Kofax.
Good luck!