The SP-01 is, indeed, a combat pistol. It is part of CZ's Law Enforcement series and was designed with law enforcement, special weapons units and military in mind. I have found the SP-01 utterly reliable. The grip frame is identical to the CZ 75 you mentioned having handled. It is not hard to handle at all. I have medium sized hands and my grip is secure and comfortable.
The SP-01 is fun to shoot due to the front heavy design. Recoil is truly minimal in the 9mm version which I own. The pistol is available in .40 S&W and would, no doubt, out handle many lighter polymer based pistols. Due to the full length frame/slide contact, the action is tight and there's little room for dirt and crud to enter the system during hard use.
Thankfully, the SP-01 has the same internal mechanisms as the P-01 and will perform every bit as well as your compact companion. ISO 9001 standards are also the same for both guns and parts are interchangeable.
CZ is undervalued in the US marketplace. I wish you luck in finding a dealer who carries the gun so can feel for yourself. If not, you'd do well to take the leap of faith and order one is you are very fond of the P-01. Prices for the CZ will only go up in years to come.