It will be a vastly faster than your 6600gt. You will have very little problems except for maybe heat but that is normal but avoid the low power version since they are very problematic. Try to find a 55nm version with 6pin power connector since they run cooler and overclock better.
Brand loyalty will never help you... only hurt. Try to think about that with as open of a mind as possible.
I've owned multiple ATI and Nvidia GPUs. Currently I have an Nvidia 8800 GTS in my laptop and an ATI 5850 in my desktop... both are great. I think that Nvidia still has an edge in the mobile GPU market... but desktops? ATI owns that segment. That explains my purchases... I guess that makes me a switch hitter. Value trumps brand loyalty in my book.
A 9800GTX+ is roughly comparable to a GTS 250 except it will use more heat and power I believe. NewEgg has 512MB versions of the GTS 250 for as low as $109 if I remember correctly; that's your best bet.
What are the rest of your system specs, The Cloak?
I ask because the 6600 is an old card, and I'm not sure if your system has the CPU power to drive a 9800GTX, or, indeed if the motherboard has a PCI-E slot. Also bear in mind the 9800 needs more power than a 6600GT, does your PSU have the connectors and output on the +12v rail/s to power it?