I have no experience with TBH's so I can't say anything regarding advantages or disadvantages in comparing the general management of either. However, from the efficiency standpoint, it seems to me that Langstroths have the upper hand.
First of all, manipulating a comb that is strongly attached to a frame on several edges and usually strengthened by wires or plastic sheets between the wax foundation is a lot less likely to get broken upon examination. Whereas the TBH combs must be held only vertically, langstroth frames can be held horizontally too, making examination of both sides easier and less likely to result in broken combs.
Secondly, Langstroth frames are made to fit into extractors (or more correctly, extractors' dimensions are made to accommodate langstroth frames) and enable the extraction of honey without damaging the combs, allowing their re-use. Said differently, Langstroth frames are made with honey production and comb preservation in mind, TBH's can't compete on those scores.
Issues such as cell size are irrelevant in comparing the two methods, since TBH's can be given wax foundation as starters forcing the bees to build cells of a chosen size and Langstroth frames can be placed in supers without any foundation, allowing the bees to build cells to any size they choose, yet still build them so as to encompass the foundation wires for strength.
Of course, when one talks about hives that get transported "cross country", there's no comparison in my mind. Langstroths are more compact, more efficient with their space usage and less likely to suffer comb breakage on route.
So, as I see it, for the backyard beekeeper, the choice is not so much an objective one as a subjective one. The beek raises bees in the kind of hive that suits her/his fancy.
