Does it have to be open-source? If free, but not trainable and restricted to Windows apps/phone is good enough, then I recommend the Microsoft OCR library. It gives you very, VERY good results out of the box. An excellent piece of work from Microsoft Research. To test it, see for example https://ocr.a9t9.com/ which uses Microsoft OCR inside.
How does the PDF OCR process compare to images? I uploaded a sample PDF with very clear sans-serif text (printed to PDF from a webpage) and there seems to be some odd substitutions. "prohibitecL" instead of "prohibited", "ac" instead of "QC" (as part of an address), random clipping of the first letter in a few lines and random use of a capital i instead of 1.
Overall very good, I'm just wondering if the library is better with image files than PDFs?
And for comparison, an OCR application with Tesseract inside: It has a dramatically lower text recognition rate: http://blog.a9t9.com/p/free-ocr-windows.html
(Disclaimer: both links are my little open-source side projects)