I don't think either are known for their customer service. CZ used to have a grumpy old guy working in customer service, but he may be gone by now. I've owned quite a few CZ rifles and they were all shooters. Stocks may need relieved or something else minor, but they are good guns. I also own some some Tikkas and they are good too. Really smooth out of the box and usually quite accurate. I'd choose either brand over a new Remington rifle, and I used to love the Remingtons.
Bergara would be a solid choice too.