Why are you stuck on those XFX cards in particular? Both of them are crippled with slow memory. A good 4670 should have ddr3 memory, and a good 6670 should have ddr5.

I have a Dell version of the Radeon 6670 1gb with ddr5 memory, and it has enough performance to be a decent XP gaming card, somewhere on the level of a Geforce 8800gt or slightly faster, while running much cooler and quieter. If you're considering that version, be sure to get one with the blower type fan, and not the one with the red fan in the middle.

Both Midtown Madness 2 and Sheep, Dog 'n' Wolf were launched as pre-XP games. MM2 being DX7.1 and SDW being DX8.

Have you tried running them with dgVoodoo2? The Radeon HD 4670 you listed is still a DX10 card. You'll want to look at even older cards or possibly a Win98 build for that generation of games.

I had a 6670 back in the day. It was good for playing skyrim at medium detail at 30-50fps. It is a decent enough choice for XP I think .

I think it is unlikely that a change in graphics will fix your issues with old games. Would be better off looking into patches or API wrappers.

Keep in mind that you are talking about low end/entry level cards, if you want compatibility with older games and performance, you should look for older mid range gpus at least.
The 4670 should be more compatible with older games (older drivers) and with windows XP you are limited to DX9.0c, DX10 is posible but unoficial.
A good choice in Ati is the HD5770, fifty percent more powerfull than the the 6670 can find one around for 30€ or less, and the drivers are the same.
And in Nvidia the gtx460 is also a good choice in the same price.
Those are mid range cards and have enought power to let you play almost any game designed for XP well.
I use a 5770 in one XP machine and it could run Rage (2011) around 30fps at 1280x1024, and I'm playing Resident evil 6 (2013 in windows) maxed out with only a core 2 duo T4500.
Here you have a good reference for the grafic cards, https://www.techpowerup.com/gpu-specs/radeon-hd-6670.c406 if you don't understand the odder charts, pay atention to the "Relative performance chart" it's not 100% perfect or exact, but it's a good reference.
Anyways, in any generation of cards, look at least for a mid range card if you want to game, that's my point of view of course.