Good that you mentioned priorities, but it would be much better to include pros and cons instead of either/or, since as you stated, your camera choice depends on your use and priorities. Yes, the Sony X3000 has superior stabilization because it uses a mechanical system as compared to the GoPro's electronic stabilization. However, that's a benefit most won't notice until you reach the extremes levels of camera shake.

On the other hand, GoPros have moved to a more prosumer level of technology since they now offer the most flexible post-processing of any of the other action camera sold. Also, because they started the action camera popularity, they additionally have the widest variety of accessories (which is why most of the knock-offs have copied their form factor) available.