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Your P-09 has the Omega trigger design, the standard P-01 has the standard CZ trigger. The P-01 Omega will have the same trigger feel as your P-09. The 229 has the smoothest double action pull of all of them, Bersa isn't bad either, but are extremely scarce to find.

I'm not really to impressed with sig triggers, you said you dont want an aftermarket trigger or an upgrade, you pypd always get the trigger polished to smooth it out. Either that or spend a bunch of money to buy a cz shadow.

Stacy, is little to no difference between your CZP09 and the CZP01. If you are not wanting any custom trigger kits/work, I would highly recommend the Sig P229 first and the Bersa TPR9 second. Cheers and you and yours stay safe!

P229 hands down then add the SRT trigger and never look back

P01 is not that much better than P09 if you are looking at the standard model. The DA and SA is a tad bit lighter by not much huge margin. Sig P229 will have a better trigger out of the box. However, I recommend checking out Cajun kit for your P09. It can significantly improve your P09 trigger without having to buy a new gun. Check it ( https://cajungunworks.com/product/p-07-p-09-pro-grade-package/ ) I hope this helps