As someone already said, the primary (the 3" on in the picture) is from the crank to the tranny. Unlike japanese bikes, HD Vtwins and the clones (S&S, Rev-tech, etc) do not have intregral trannies like you japanese and euro sportbikes. HD transmissions are separate from the engine. Meaning which if you screw a gear in a HD tranny, its gonna be ALOT cheaper to fix than any sportbike tranny will ever be (no splitting the cases). Stock primaries are chain driven and have its own oil. The 3" primary belt drives are designed for teh high torque motors that could tear a single chain driven primary to pices. Also the dry clutch setup is a bit more durable with them.
As for the secondary belt drives (tranny to rim), belts are quieter than chains, more durable and less maintanance. Yes they can break, but its not common. Big drawback is to chainge rear pulleys you more than likey have to change belts too.
And belt drive has nothing to do with using a 300 size tire. Thats done by offsetting the tranny mount plate and/or moving the motor left in the chassis (which is why right drive trannies are becoming popular since you can put the motor back in the center of the frame and still get clearance for the 300 tires).