Are you gaming in hd? (1280x720 or higher resolution)
If so I honestly don't think you are going to see a drastic improvement with that specific card.
I would honestly suggest looking at an ATI 6750 it's right about the same money (around 100 bucks)
and has much faster memory in it.
the gt440 has a superior pixel rate, but I don't think this is something you want over the ability to process properly at high resolutions (texel rate/memory bandwidth.)
Neither one are high performance cards mind you but the newer ones are built completely differently than your old 8 series nvidia. ...don't get me wrong I had a 8800gt when they first came out and it was the best card on the market. I still have it though and it only sits in a drawer because it simply can't handle 1080p resolution at a liveable rate.
This is dependent on your motherboard to an extent though. While a standard pci-e is capable of running a 2.1 card, it can be buggy on some motherboards. ...and I honestly don't know if your board is good on that front or not. You could always drop gigabyte support a quick email asking if that specific card will work properly with that board, there may be a bios update involved.
anyhow some related links.
what I would get if it were me - Newegg.com - HIS H675F1GD Radeon HD 6750 1GB 128-bit GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card with Eyefinity
Comparison chart for gt440 vs 6750 ati. GeForce GT 440 1.5GB vs Radeon HD 6750 1GB – Performance Comparison Benchmarks @ Hardware Compare
product page for your motherboard- GIGABYTE - Motherboard - Socket 775 - GA-946GMX-S2 (rev. 1.0)