6670 vs Gtx 650 which is better on a PSU of 375? Will they run?

both will not run safely should they run at all. buy a quality 450~500w psu. the 6670 does not need a 6-pin power cable while the regular 650 requires one (Asus have made one that doesn't need em). if i were you, i'd at least step up to the 650 or 7750 minimum.

if your unit is a good one (not some generic one) it should be able to run the cards that you mention above. between the the two 650 is better.

HD 7750. It's what I would go with in your situation. Uses only power from the PCIE lane. Which is 75 watts I believe.

http://www.newegg.com/Product/Product.aspx?Item=N82E168...

Sapphire. Even has 2GB VRAM!

I would get the following Radeon HD 7770 for $100 after rebate. A regular Radeon HD 7770 is faster than the GTX 650. This is the 1GHz edition which means it will be even faster.

http://www.microcenter.com/product/403019/R7770-PMD1GD5...

Click below for performance comparison between a "normal" Radeon HD 7770 and the GeForce GTX 650.

http://www.techpowerup.com/reviews/EVGA/GTX_650_Ti_SSC/...

dont even think of getting a 6670....its total crap..
if you have just the two choices you mentioned, then go for the gtx 650......see if you can get a ti version...

but if more choices are a welcome, then go for a 7770....the ati 7xxx series have beautiful error free dx11 support....
but for an hd 7770, you will have to get at least a 400w psu....(that too a decent one with more than 24amps on the 12v rail)...

if you ain't planning to buy a new psu , then a 375w (if it has a 6pin pci-e connector) CAN handle a gtx 650....easily....
if your psu doesnt have a pci e connector, then in any case of a gpu upgrade , u'll have to get a new psu(look for corsair or antec 400+w)

DONT EVER THINK OF BUYING A 6670....!!

get a 7750. its perfect for your psu and its also powerful. it does not require any cables like 650 and 7770.