What is your goal? Hunting, paper punching, or competitive?
PCP is the most accurate, hands down. Of the two guys I know that shoot pcp, one owns two Walthers, and the other shoots a Daystate. All of them are $1200+. The first guy also has a Beeman Chief that he says is the best budget gun, but it's had an issue here and there. The problem with the Chief is that it's not regulated, so it has a pressure curve that you have to get cozy with to keep you shots accurate. I think it's something like 20 shots before the pressure drops off enough to kill your group. Also, you have to tweak the orifice to get it tuned to your pellet and desired shot string initially. The regulated guns keep the pressure nice and consistent and don't need as much tuning, but you have pay for it. Also, with pcp, everybody says bypass the pump and go straight to tank and find a scuba shop or paintball place for refill.
Now abour the first guy ... he is the best airgunner at our club. His son was a junior national field target champ back in the day. His son won with an Air Arms TX200 springer. IMO this is the reigning king of all spring guns. I have shot it and it is sweet. Minmal tuning required, just buy some good H&N, RWS, or JSB pellets and find one it likes. Still pricey, but as a Diana 34 and Diana 240 owner, I wish I had just gone TX200 and saved the tuning time. The TX200 almost feels like a pcp because the shot cycle is so smooth. The balance is so sweet. There are some sidelever springers that are really good, but they are older models. I would be wary of the cheap or jazzy springers as I have seen many disappointed shooters who are unaware of the in depth tuning and maintenance required. Also springers are scope killers. I have destroyed 5 scopes and finally found Hawke Optics. I have yet to break a Hawke on my Diana's, and the 34 has been wearing a Hawke Airmax for the last 3,000 + shots with zero issues.
IF you end up going with a springer, get something heavy! Then, PM me and I'll walk you straight past some seriously major headaches. They need tuning, lots of tuning, lots of experimentation, the right pellet, and a $200+ scope made for springers. BUT, my Diana 34 can now hit 4" steel at 50 yards off hand, but I have at least 100 hours (maybe 200, hell I lost track) of work in it, including detuning the velocity to 750fps. Stock screw torque, spring polishing, trigger polishing, piston and cylinder polishing, barrel droop, scope robustness, rock solid mounts, barrel lapping - these are all things I had to work out. But no squirrel ever makes a permanent home in my attic. Its deadly to 30 yards and accurate to 75 yards now. It was ugly at first though.
As far as CO2 cartridge, well, they are accurate, but jeez those guys have issue after issue. Mainly running out of gas before a match is over, or having cartridge seals just randomly go bad (in the middle of a match). That and the cartridges add up if you shoot a lot. Again, since its gas, get a regulated or you might as well just get an unregulated pcp. IMO, pcp just obsoleted CO2 cartridge.
So, you probably picked up on the fact I like the AA TX200. I just like springers cause your power source is your muscles and always filled up and ready to go. And the TX200 can outshoot most of the cheap pcp's all things considered. But, for straight up repeatable olympic level accuracy, pcp is it. Just be ready to deal with that pesky pressure curve if you don't go regulated.
Man, please don't hesitate to PM me if you want to get more in depth.