We don't generally hear casualty figures for big starships - but FWIW, the Hera in TNG "Interface" went down with "over 300 crew", and backstage sources insist that she was a Nebula class starship, thus basically exactly the same size as the Odyssey.
So perhaps "over 300" is the real crew requirement for ships of that size, and 700 of the people aboard the E-D were passengers of one sort or another.
Then again, in DS9 "Field of Fire" the starship Grissom is lost with 1,200 people, and backstage sources consider her an Excelsior, much smaller than either Galaxy or Nebula. So trusting backstage sources in identifying the size of ships for which we have dialogue casualty figures is wrought with uncertainty.
The casualty figures in TNG "Drumhead" suggest that 11,000 people died and 39 ships were lost at Wolf 359, giving 280 people per ship. Most of the designs seen in or after that battle were between Excelsior and Galaxy in size. So perhaps this is further proof for the idea that big ships may go to battle with just some 300 people aboard?
Timo Saloniemi