+1 @zooted. The GT440 isn't really a gaming card. A GTX660 or HD7870 would be nice strong upgrades. The former uses a little less power, and the latter generally (but NOT always, e.g. BF3) is a little stronger in games.
If you're a bitcoin miner, AMD cards are the ONLY way to go.
You might find a used HD6950 for a good price. Be careful of the used market, but a working HD6950 would be a decent upgrade. On the nVidia side of the house, a GTX560Ti would give around the same performance. Note that some games favor one or the other, AMD or nVidia, so check benchmarks.
It would be about the same performance wise, but it would be less heat and power. It would also leave you another spot to add another card. You would have to get to a 7870 / 7950 to see any major improvement.