Yeah, they are very similar. The fabric is pretty much the same - knit, like a quality t-shirt. The main differences are the Moby has tapered ends and matching thread for the stitching, the BB has square ends and a contrasting thread for the edge stitching. The only benefit to the tapered ends is it's a little less bulk when you tie your knot. As for the stitching, that's all a matter of personal taste. I say choose based on whichever one offers the colour you like best.
Oh, the BB also comes with an instructional video, but honestly I didn't find it very useful at all. (Contrast that with the video that comes with the Hug-a-Bub, which is awesome!)