Location: Hicksville, NY (Yes, it's an actual town).
SEWER BACK UP, Which Flood Control Good?????
INSTALL BOTH! EEEEWW..
Seriously though, I've (thank everything) had no experience with this situation, but with the first solution I'm thinking there could be an issue with your local codes about putting pressurized waste directly into the sewer main. On the other hand, if the company sells/installs it in your area, it's probably kosher. (And if the muni sewer was backing up into my basement regularly, I'd be more concerned with my basement than the muni's code).
A backflow prevention device (as in both systems) definitely seems like a goooood idea.