I haven't checked to see what card is more powerful, and I'm not going to. But you should really just get the most powerful card you can with your budget and ignore all of the DX11/energy efficiency/PhysX stuff.
I really doubt that you are going to be playing games in DX11 with a weaker card like the 5670. You would definitely have to turn down some details, especially if you are playing at a sizable resolution. If I was you, I would rather just play in DX10 with the details cranked back up.
I don't know too much about PhysX performance impacts, but I am guessing that the situation will be very similar in regards to DX11. Your card will not be powerful enough to handle PhysX without turning down some settings. If it was me, I would rather play with the settings cranked back up. So, just like DX11 with the 5670, PhysX with the 9800GT should be discarded from the list of features you take into account
Energy efficiency? As long as the card isn't adding sizable increases to your electricity bill, I would say screw efficiency. At the end of the day, you want the fastest card you can get for your money.
I'm assuming based on some of these other posts that the 9800GT is faster, so I would say get the 9800GT. If they were both equal, I would definitely get the 5670. If the 5670 is more powerful, well you get the point.