A lot of people thought that the 681 was a cleaned up version of the 7900. The official word was something to the effect that solo and dolmar worked closely in early development of their new 60-90cc saw families, but then things went south. Regardless, both of them look very close. If you do a search you'll find a lot of stuff.
The solo has their very basic but functional prefilter system (nice nylon screen that takes care of large chips). In addition to what snelling said for improvements/advantages over the dolmar, supposedly the AV mount from the handlebar to the P/C mount is beefed up or less prone to breaking. Again, relatively minor stuff.
The real downside I see is that there are a lot of aftermarket P&C kits and parts available for the dolmar saws. This does not seem to be the case with the solo, at least from what I have seen. I think you'd want to do careful research before you assumed that any parts were interchangeable.