Here is a small situation for which your 6200 may have an advantage (until October): simple video decode using VDPAU in (for example) MythTV in Linux. I saw (via the shortbread) in Phoronix that AMD have released code to expose the UVD under VDPAU, and more recently, the power management too. They should be in the kernel and open source drivers in October, hopefully. I'm not sure if the 3450 had UVD, I have a suspicion that came in around the 4000 series. But, if you want to watch 720p HD TV signal from your Linux computer, you may be able to do so slightly more efficiently than with your 3450.
(This is from when I looked at it some years ago - I hope what I understood then and remember now is correct; but AGP was a long time ago and I'm not overfurnished in the brain department so may have the wrong end of the stick.)
All Radeon HDs with the (possible?) exception of the 2900 series had a UVD block. Once that support is in and working the 3450 wouldn't be bad for a home theater PC, but I wouldn't use it for much more than that and desktop compositing.
What I'm baffled by is the assertion that the 9600XT "refreshed slowly" at 1680x1050. I wouldn't doubt that the 3450's featureset is better at this point, but there's no reason a 9600XT shouldn't offer a decent experience for basic desktop use unless there's something physically wrong with it...
Dude you need a new computer. 3rd world country people have better computer than you.
Be nice, people keep old rigs alive for lots of reasons. He asked a question, and we've all told him that he's basically downgraded. No need to tell him he's worse off than a "third world country [person]," whatever the hell that's supposed to mean.
Workstation: Ryzen 1700X, 16 gigs DDR4-2400, RX 480, Win10 Pro x64 / Xubuntu 17.04
Plaything: 2008 Mac Pro, 2x Xeon E5462s, 6 gigs ECC DDR2-800, GTX 660 Ti, El Capitan / Win10 Pro x64
HTPC: i3 4170, 8 gigs RAM, Geforce GTX 1050 Ti, Windows 8.1 x64