Which one these is the better graphics card?

The GeForce GT440 is better than the 5570... even the older GT240 is better than the 5570. Having 2gb of memory isn't useful for a low-end card like that, because anything over 512mb is only utilized at very high resolutions (1920x1080 and higher). However, these are $75 cards you're talking about.... nothing in that price range will be good 3-4 years later unless you're just using it for regular work, not gaming. You'd need at least a $150 card like the Radeon HD 5770 if you wanted it to still be ok for gaming 3 years from now. Here's how the 5570 compares to other entry-level cards: http://www.techspot.com/review/245-ati-radeon-hd-5570/page5.html

NVIDIA GF GT440 is more powerful... but I doubt it'll last you for 3 years. If you can afford it, go for GF560, 570 or 580. Or if you're looking into AMD/ATI options, go for 5770, 5850 or the new 6000 series. Do take into consideration, the more powerful gfx-card, the more power it consumes. So make sure your PSU can handle it.

2GB ATI Radeon of course. It is obvious, the higher memory always wins.