There isn't such thing as a single tool or one workflow for colour correction. So if I start telling people what is "best" for them isn't much help since there are custom factors and parameters involved. Personally I'll skip Davinci Resolve.
I've used many times AF to export a dedicated LUT either for colour correction or just a creative look and it never failed me.
For LUT import in FCPX there is an excellent LUT loader that you can get for free. It is available thanks to people at motionvfx.com. It can be found here.
It makes me happy that creative professionals, have a plethora of tools at their disposal these days.