The usual P01 you see is the model with the decocking lever on the left side of the frame. I've never held one, can't tell you how easy/not easy it may be to operate the lever.
The newer, and not so common P01 is the Omega model. It comes set up with ambidextrous decocking levers that angle forward, just like ambidextrous thumb safeties. In the box with the new Omega should be a set of ambidextrous thumb safeties for cocked and locked carry - or, as some people do, safeties so they can carry it at half cock or hammer all the way down on the back of the slide.
The frames on both models are aluminum with grooves in the front/back of the grip. That is what makes the difference for me. I have a nice CZ75 Compact I used to carry. Then I got an Urban Gray P01 (the first model of the Omega P01's - set up with a threaded barrel/barrel protector and suppressor height night sights, in case you want to buy a suppressor, or just like the look. I didn't carry the UG P01 long but there is just something about the way the grip feels/fits in my hand. I immediately get a feeling that this one is "right" for my hand. I eventually bought a black P01 Omega and started carrying it concealed and open carry (only around my house/property). I still carry the P01 Omega (black) on road trips so my wife's CZ Compact can use the same magazines as the pistol I carry..
There is a difference in weight between the CZ75 Compact (steel frame) and the CZ P01 (aluminum frame) but I don't believe I really notice it. The P01 also has the light/laser rail and the CZ75 Compact doesn't (unless you come across one of the CZ's marked CZ75 Compact that has a steel railed frame like a P01 (no grooves in the front/back of the grip frame though.)
I bought a couple of the little PL Mini's to put on my P01 Omegas so I'd have the same lights on both pistols.
My UG P01 is my basket pistol. The basket by my recliner in the living room. When the doorbell rings at night, or we hear a loud noise somewhere inside/outside the house I grab the UG P01 and go take a look.
You can get 16 round magazines for the CZ Compacts. It's a 16 round magazine (like the full sized CZ75 uses) with a floorplate on it that fills in the gap between the bottom of the longer magazine and the frame (some people object to that look.) That gives you 16+1 in a compact carry pistol for a small amount of extra length under the frame.
Urban Gray with the 16 round magazine and black with the 14 round magazine, for comparison.
