Even when the source is 24fps in both cases? You're not getting any more information in 2D, just usually refreshing the same information or at best (/worse) generating intermediate information to overcome any particular limitation in your display technology regarding image retention. Active shutters should theoretically do at least as good a job of that kind of thing if you want it, while depending on the TV you might get a better image if you sync with the material frame rate anyway.
I completely take on-board azy141's comments that 3D broadcasts are inferior at the moment due to bandwidth constraints. That doesn't have to be the case though for films through blu-ray or internet.
True that you could instead use the bandwidth to double the 2D information - but experiments like The Hobbit HFR suggest we're not there yet. 4K however, I think would be better
