I apologize in advance if this has been asked before, but I know that this film was shot in both Todd-AO and CinemaScope, both being quite different in performances and energy. My question is: what version is on the current DVD.

It's 2.20:1 and that is theTodd-AO aspect ratio. Each scene was filmed first in Todd-AO and then in CinemaScope. You probably are aware that the Todd-AO version is the superior one.

...And it's non-anamorphic, so beware.
The only Fox Rodgers and Hammerstein musical on DVD that is anamorphic is the Sound of Music, FYI. Here's hoping all these get anamorphic rereleases very soon. I have heard mumblings of a 40th anniversary Sound of Music SE with a new transfer to be released sometime late this year.

Sound of Music going OOP and more news you already know

There have also been rumors of an OKLAHOMA 50th anniversary edition later this year featuring both the Todd AO and the Cinemascope versions of the film.

Most musicals of this ilk tend to make me want to pour saltwater in my eyes, but somehow I have a soft spot for Oklahoma. I lived out there in my childhood for a bit, but it's something more than that. I've been waiting for a 16x9 version to pick up the DVD though.