With 3d movies, you will always find a small dark area on one or more edges of the screen. The reason for this is the way the 3d Technology requires "two or more" of your size screen, offset from each other slightly to produce the 3d images. So the only possible way to put to offset images, is to have each one be smaller than the overall screen. This SHOULD be very small, however - one of those things that you only notice once you know about it.
In general, however, there are several different formats of HD Movies published - many of them have different aspect ratios - some, like Lord of the rings have a 1.21 ratio which is extremely long and "short" from top to bottom. The rest of this spaces is displayed as black - many refer to it as shadowboxes - but I think that inaccurately describes them. They are actually just empty areas that are not covered by the cinematic film ratio of length to width. Very rarely will you see a BlueRay that exactly fits a 16x9 screen - because, of course, our 16x9 standard doesn't match any cinematic standard!
All that being said, then it is possible that if this doesn't describe what you are seeing the "cheaper" player isn't processing the 3d correctly. The screen relies a great deal on the proper processing of several different types of 3d to display the screen properly. It sounds like you may not be getting, to the TV, what you need to correctly create BOTH images (remember that 3d is two FULL HD images, overlaid, so something as simple as inadequate HDMI bandwidth on a cable, can destroy the image. So can many other things. Make sure you don't have any devices along the HDMI path, like a switch or a selector. Anything in that path can cause a problem with the bandwidth and that will be first obvious on 3d.