Best way to stabilize footage?
Because software stabilization methods cannot compensate for the shifting parallax of a shaking lens, they will always produce less than ideal results.  In my experience, FCPX's stabilization is just as good as other software packages (I have experience with Shake and After Effects as well), and they all basically work the same way.

This is probably not the answer you want to hear, but the best way to stabilize footage is to shoot stable footage in the first place.  Software stabilization is really just analogous to fine grit sandpaper; It's a good final step to add polish, but you'd never use it from the start.

Physically steadying a camera can be expensive, but that's why audiences have learned to appreciate stable shots -- they associate stability with quality.  But of course you know this, or you wouldn't be asking.

But there are good, reasonably priced ways to physically steady a camera.  Where I work, we have dollys, sliders, shoulder mounts, tripods, brushless motor gimbals, camera cranes, clamps, arms, and pretty much you name it.  But in my experience, the most versatile, portable, practical, and cheap piece of kit that we routinely use is a monopod.  It doesn't allow for all of the fancy movements of the other stuff, but nice ones will at least let you do a fluid pan.

Sorry this doesn't help with footage you've already shot, but I hope it helps with future projects.