As Ben said, but I do actually think that the stabilise function in the free Davinci Resolve version gives often best results (but not always). I do not see much difference between the build in stabilise in FCP and Coremelt, specially for tricky shots.
I have some shaky shots I need to stabilize. I've used FCPX but I find it a bit lacking in that department. Anyone have 3rd party software or plugins they'd recommend for stabilizing?
You can try various stabilizers but it's unpredictable whether one will work better on specific footage. It is often a trial-and-error process. Overall I like the one in Resolve best, but it requires exporting round-tripping footage. The plugin-based stabilizers are more convenient. I use all of the below:
DaVinci Resolve. Available in free version which works very well, but an upgraded stabilizer is in the paid Studio version. Resolve has multiple stabilizer methods. There is a simple method within the Edit page and more complex ones in Color page's tracker window:
I also sometimes try Premiere's Warp stabilizer but I like the Resolve one best. I usually try the built-in FCP stabilizer and the plugins first, then if those don't work well I round-trip the footage to Resolve.