Hitch -- definitely not calibre, as calibre doesn't have any OCR capabilities at all.
Google's open-source Tesseract engine (with various frontends) is supposed to be the best freely-available OCR and is also cross-platform.
But there is a reason why ABBYY Finereader costs so much money, as you said, it really is better and is worth the money.
(Gah! PDF conversions... here is calibre's
official warning about PDF.)