The PC tells the ECM to deliver X amount of fuel, in ratio to the throttle position, which delivers Z amount of air, with your engine, exhaust system, and air intake. Depending on how the tuner tunes it with the fuel you have in the tank that day, he may tell the PC that he wants the air/fuel ratio to be 13.5, all the time, at certain throttle positions. But, if you get different fuel...for example it has more enthanol in it...you won't really be running 13.5, it might actually be 14, or whatever the combustion properties are for that load of fuel. With the O2 sensors, the ECM can adjust itself for that different fuel, to maintain let's say, and air fuel ratio of 14.5:1 at cruise turning 2800 RPM. The PC can't do that. It's much more complicated than that, but that's a simple way to understand what's basically going on.
I ran PCIII's on both my '06 SEUC and '06 SEVROD...worked just fine. However, compared to what you have on the '10, it is crude at best. Proper programing (tuning) with the tuner you have, or something like the TTS, will allow you to have the best of both worlds...good fuel economy at cruise, richer at idle and wide open throttle, and the ability to adapt to changing fuels and conditions. There are limits with the HD system, due to the narrow band O2 sensors, but it's still a better way to get there, IMO, than a PC. But that's my opinion...and that of many others.
BTW...I've never owned a softail, but I'm pretty sure you've got the B version of the 110" motor because the motor is not rubber mounted like the touring bikes. It's counterbalanced internally. I think I'm right on that, but somebody correct me if I'm not. The B motor will never develop quite as much power because of it's design...not significantly different, but different. The counterbalancer eats some power.