I ride a SS probably 90% of my rides. I have gotten stronger, better leg definition, etc than when I only rode a normal road bike. You have to push harder on the hills and into the wind, which sounds bad but strangely, you get used to it pretty quick. I ride for fitness and fun, and I seem to get a better workout in less time; no solid evidence but a 1 hr ride on my SS physically feels like a 1:15 minute ride on my racing bike (which may be a reason not to ride a SS if high mileage is your goal).
It's lighter - no derailleurs, 1 chainring, etc. It's quieter - I don't have the click-click-click noise. And it feels different pedaling than a derailleur'd bike - like a more direct connection between legs and wheels.
Less stuff to maintain.
Plus it's really fun - you don't notice how much you think about shifting until you don't have to. Let's you enjoy just riding a little more.
As for one over the other - get one of each if possible. Otherwise, if you are riding for fun and fitness (and not a too hilly area) I endorse SS. If you are doing high mileage and long group rides like centuries, I would get a multi-geared bike. You could always just not shift it. 🙂