I think Bethesda does great visual storytelling - the things scattered about Skyrim and Fallout 3 that tell their own tale are just fantastic - and they also do pretty good writing in terms of lore books and things like the Keller family transcripts. I don't like their narrative storytelling, however, I find it loose and insipid. I think it's largely as a result of having a style of game that allows you to go anywhere, kill (almost) anyone and be any kind of character you want, I don't think that lends itself to a tight narrative style. I can get behind that to a certain extent, but I tend to bore of it easily.
I find Bioware's narrative storytelling to be more memorable and engaging than Bethesda but they don't do as well at the little visual details that make a world breathe, imo. Bioware's forte is characters - they are what makes Bio worlds breathe and they do this far, far better than Bethesda. I also think Bio are leagues better at dialogue, and I find their worlds (Dragon Age and Mass Effect universes) more inherently compelling than Tamriel which I find kind of bland. I do prefer the Fallout setting overall, but Bethesda can't be given credit for creating that
Imo Obsidian have both companies beaten for storytelling - at their best (new Vegas, Mask of the Betrayer, and for me Alpha Protocol), Obs creates experiences that are very difficult to match for me - but even so, I think Bioware just edges them out for characters (which is really the main reason I love Bioware games).