Depends on the rest of your system really, but I have used an X850XT which has performance about the same as an X1650XT in most games, and the X1650GT is basically just an underclocked X1650XT which you should be able to overclock the gt to the same clocks as the xt. My X850XT with only a AthlonXP 2800+ and 1GB of generic DDR could run HL2 and EP1 at high with anti-aliasing and anisotropic filtering at 1024x768, so you should be fine with running high at that resolution.
Yes, it was a 256Mb card and also the AGP variety, but that doesn't make much of a difference as it has the same specs as the PCI-E version.
you might want to look at the 6800 series. not sure they fit into your $80 budget, but if you could extend it to around 100 and find a 6800gs, that might be a good option. i had an old 6800gt and until i killed it, it played a lot of games at high settings on the res right above yours. im not sure if it out performs the 1650 pro in all scenarios, but on the vga charts on toms it wins in the doom 3 and bf2. good luck
As for the 6800 performance BF2 and Doom 3 tend to be nVidia oriented performance wise anyway. The X1650GT is closer related to the X1650XT then the X1650Pro, because it has the full amount of hardware units that the XT does, with 24 pixel shaders, where as the pro only has 12 pixel shaders. The Pro also half the number of the other major hardware units compared to the XT(with the exception of vertex shaders where Pro has 5, XT has 8). If you choose to overclock the X1650GT, you will most likely get to speeds of a stock X1650XT which on average outperforms even the 6800Ultra.
Here are few cards which are better than X16xx series and trust me, they really are! http://www.newegg.com/Product/Product.aspx?Item=N82E16814102700 http://www.newegg.com/Product/Product.aspx?Item=N82E16814134019 http://www.newegg.com/Product/Product.aspx?Item=N82E16814161179 http://www.newegg.com/Product/Product.aspx?Item=N82E16814186025 http://www.newegg.com/Product/Product.aspx?Item=N82E16814186025 http://www.newegg.com/Product/Product.aspx?Item=N82E16814130062 http://www.newegg.com/Product/Product.aspx?Item=N82E16814130063 http://www.newegg.com/Product/Product.aspx?Item=N82E16814121082R One of them is 6800GS DDR3 version. I own one( check signature) and i am running NFS - MOST WANTED with everything maxed out settings on 1280X1024 resolution without any problem...even Splinter Cell - Chaos Theory and NFS - Carbon (2X AA)! THey say 7600 GT is better than 6800GS but i say 2600 XT is much better than 7600 GT and also it also holds the advantage of DX 10!
And the card I'm looking at has 24 pixel shader, 8 vertex shader, and can easily over clock. Also http://www23.tomshardware.com/graphics_2007.html?modelx=33&model1=734&model2=858&chart=318 there performance is just about the same. and theres no point in me getting a really high end card. Turns out some guys made patchs that fix the problem with thief1/2 and system shock 2, so maybe some one knows a dx10 card thats about the same price but is better?