I can't comment on the SP-01 as much as I can on the P320. I own P320's but my only experience with the SP-01 is from shooting my brother's. I am heavily biased toward hammer-fired guns. I've owned a lot of Glocks and Springfields, but divested myself of them all and had went strictly back to hammer-fired guns of the H&K, Sig, and Beretta flavor. When the Army choose the P320, I had to grab one to see why it won out over the others (being that Sig is known for hammer-fired guns). I first purchased an FDE Compact in 9mm after they made the change to the gun to address the drop safety issue. The out-of-the-box trigger is much better than Glock triggers and can be made ever better with some of the APEX kits. I really like the modularity of the platform. The gun feels great in my hand, it's accurate, and so far I haven't experienced any issues/malfunctions through the few thousand rounds I've put through it. I have heard that the P320s don't really like steel-cased ammo, but I never shoot steel-cased ammo, so I cannot comment on that. My normal EDC is an HK P2000sk V3 in 9mm, but recently I have toyed with the idea of switching over to my P320 Compact for EDC with its higher capacity, good size for AIWB carry, and nice trigger for a striker-fired gun. I've been carrying it the last few weeks and am thinking I will probably make the change. While I haven't actually weighed the two side-by-side, even though the P320C is a little larger that my P2000sk and has a higher capacity (+5 rds), it feels lighter when carrying than my P2000sk does (though this could be due to using two different holsters)...
If you're looking for a carry gun I would go with the P320C or X-Carry out of the two options; however, the CZ P-01 is a pretty nice compact for a hammer-fired carry gun. If you're going for more of a competition gun, I would go with the SP-01 due to my preference for hammer-fired guns.