The P01 may be more accurate with the ammo you shoot. Might try different brand/bullet weight in the SP01.
Could be sights, trigger, barrel to slide to frame lockup. CGW barrel bushing for the SP01? One of my compacts didn't need one and the other one needed one real bad.
No reason a shorter barreled pistol (or rifle) can't be as accurate as the longer barreled versions.