For most content any escort will beat the Vesta or Ody in the efficency battly. Any escort can solo an elite borg cube (not neciserily a tactical, at least not without taking forever). So tanks and science powers are generaly a needless sacrafice that hurts a teams ability to beat an optional timer through the sacrafice of dps.
That said, any optional timer can be beaten without a single escort provided the people in your team know how to squeeze the most dps out of their cruisers and science ships and know what they are doing.
So assuming we are going for fun over efficeny your choice should realy be the Vesta. The only thing an Ody can do better is the ship healer role.
Some will disagree with me and say it tanks better as well, and thats true if your hull tanking. But with sheild repair units, a better shield modifier, and 5 or 4 science console slots the vesta will easily out shield tank the ody.