Which is stronger

I have no experience with a 9 1/4 so I can't comment on their strength. If your car is light weight, auto and doesn't hit the tires hard the 8 3/4 may be fine. Mine broke on the second pass after installing the 408 in my 3260# Dart. It couldn't take the 1.38 60'. After removing and disassembling the 727 to check the sprag I rebuilt the 8 3/4 and promptly sold the complete rear end. My Dart now has a Strange S-60 in it.

You can find 9" parts pretty cheap and IMO it's a better option than either rear you have for a car with decent HP.

As far as parasitic drag goes I don't think anyone on this board with a street or street/strip car would notice it.

Just the guy I was thinking of! Did you post up on the Strange installation?
I don't think I would recommend the 8-3/4 for anything over 3000 while doing race duty.
Sure, you can brace them and swap to discs for lighter weight and .....
As the been there and done that crew here always states, do the DANA over the 8-3/4. Cheaper out right IIRC over a modified 8-3/4.

I have a 9-1/4 in my Magnum. But I'm not pushing it at all.