Yes, they are different, at least a little bit. I just did a quick test using a rocky beach scene I shot handheld. I tested Final Cut Pro X (v.10.0.6) and iMovie (v.9.0.9) and used their default stabilizer settings (which in iMovie are basically all you have). Looking at the results, FCPX does look a little bit better, but not by a significant amount in my opinion. Where FCPX really makes itself useful is in the ability to adjust parameters of the stabilization. With iMovie, if you don't like what the app did, you're pretty much stuck. With FCPX, you can do more tweaking and testing to help get things right.
Another, smaller note: iMovie seems to lock you out of using the app while it is calculating and applying the stabilization, whereas FCPX will do it in the background and will allow you to still work as it computes.