The GT 240 is the obvious better choice, it is slightly slower than my 9600GT which I have in my HTPC.
I would probably go for the HD 5750 vs. the HD 6670 since it's raw performance is greater. Since the HD 6670 is a 2nd generation DX11, it is probably a little more efficient at processing DX11 effects. But the HD 5750's raw performance should still make it faster in DX11 games.http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&Description=HD+5750&x=0&y=0
Note: If your motherboard only has a PCI-e version 1.0 port, then I don't recommend installing a PCI-e v2.1 video card since the HD 6670 and the specific HD 5750 (which I provided to link to above) are both PCI-e 2.1 cards.