Depends what you want.... if you need superior 2D visual quality, DVD playback, and TV-Output then the Radeon will likely suit you better. For the most part it performs pretty closely to the Ti4200 in current games, but it'll likely fall a bit further back in future games.
The Ti4200 will offer slightly better performance in current games, and will be better suited to future games if you intend to keep the card for a long time.
If your only going to have the board for a 8-10 months or less I'd probably go with the R8500 as it's cheaper, fairly competitive performance wise and it's a more well rounded product.
If gaming is the main criteria then the Ti4200 would be a bit better though, and if your looking at keeping the board for a year+ then it'll likely start to open up larger performance difference between it and the R8500.
It basically comes down to what you need in a graphics card, both will offer solid performance at a competitive price.