Rick is correct there are lots of controls to change the output. by default warp stabilizer uses a combination of imaging resizing & cropping in order to achieve the stabilization. these changes in scaling/croping will change the quality of your image, so unless you are working on very large size footage you'll probably want to export to 1 size smaller format than your footage you are trying to stablize. (e.g. if your footage is 1080p export it as 720p).
Hope it helps
As Rick said, you probably may only want to use position, rotation and scale in your case and handle the rest by other means. The Warp Stabilizer operates based on edges, so almost inevitably it will always try and straighten contiguous edges it finds in any imagery.