I have a PMD670 as well as an Oade WMOD 661, and I am familar with the PMD671 through friends that own them.
Biggest differences: PMD671 has -10 db sensitivity unbalanced RCA line inputs, PMD661 has mic/line switchable balanced XLR inputs. This gives you two advantages, a +4 db sensitivity balanced line input, and Doug's performance upgrades improve both mic and line sources, as opposed to only improving the mic in on the PMD671.
The PMD671 has digital in and out, and the PMD661 has only a digital in. Unless you require a way to output digital for a patcher, this is not a big limitation on the PMD661, IMO.
The PMD670/671 has a weak internal battery solution. The sleds can have contact problems from jostling the bag, causing premature low battery indication or total unit shutdown. The PMD661 can run for many hours with just 4 rechargable AAs, and because the batteries seat directly into the recorder, jostling the bag or the recorder itself will not impact the battery contact.
The PMD671 has a margin indicator with a reset, so you can check how high your levels were hitting while you were away from the rig, for example. The PMD661 does not have this feature.
Lastly, the PMD661 is more than half the size and weight of the PMD671. I am sure there are other differences I have failed to mention, so anyone else please chime in.
I love carrying a smaller recorder in a smaller bag. My PMD670 has been relegated to the role of DAT transfer device to archive them on wave files since I moved to the PMD661.
Good luck!!!