With level up and drive off, they are all pretty much the same. Just pick up whichever one is available.
With the drive up, they're all pretty much the same too. The difference between the 808 and 9 variations is a couple of resistors towards the output stage. The clipping stage is the exact same.
Not sure what the Maxon OD808 is. I've read TS10 too, but I've also read it's actually based on the original 808 (the one with the narrower box and the ugly artwork on the sides). Whatever it is, in my experience, it's slighly less mid-pushed and broader compared to the current RI TS808. That being said, it's still like 98% the same. Only if you compare them side by side, do you really hear the difference. And it's certainly not as open as some of the current more modern tweaked TS-types.
The Maxon OD9 is the TS9, but with the output buffer removed. Still very similar-sounding, but slightly more open, IME. It's also true bypass.
I'm not sure about the TS Mini. But AFAIK, it's close to the TS808 circuit, just with SMD components and in a smaller enclosure. It's also true bypass, so not sure what they did circuit-wise for the switching compared to the Maxon OD9.
But it's only if you're actuall A/B'ing them that you notice the differences. A TS9 and a TS808 are way closer to each other than a TS9 or 808 is to a Boss SD-1, for example, even if the Boss SD-1 is relatively similar in the grand scheme of things.