Xs1 / hs30
My experience with the X-S1.
There is some freeze before the picture is taken (burst mode or not). If you have everything in manual (no AF, no AE, no Face Detection, no Face Recognition, etc), the freeze will probably diminish/disappear. At first, the freeze bugged me. Now, I live with it.
There is also an effect that is sometimes known as the slideshow effect. In burst mode, the camera displays the previously shot picture and not the "real time" image. If you are shooting at 10 frames per second, the previously shot picture is not that old. If you are shooting at 3 fps, it gets very annoying. (Anyway, even at the 10fps setting, after the buffer gets full (after about 10 images or so)l, you will end up at 3 or 4 fps.)
Check the reviews on dpr. I think the section is called performance. You'll see that even cameras as OM-D or Sony a77 have slideshow effect at some stage.
Bottom line. If it bugs you and you make the switch to the X-S1, don't expect a "perfect" camera as regard "freezes".