I'm surprised AF works with the 6D! That lens was discontinued at least a decade ago. Being that it does work on the 6D, though, it is disappointing that it doesn't also work on the 70D. Both the 6D and 70D use the Digic 5+ processor and were released about 9 months apart in 2012-13 around ten years after the Tokina AT-X 400 AF was last made. It would be interesting to know if the lens would work on the 7D. The 7D is very similar to the 70D in terms of still photo performance and the AF sensor design but was released in 2009 with dual Digic 4 processors.

If the 70D at least recognized the lens and allowed you to control the aperture I would say the problems focusing are likely due to the fairly narrow aperture of the lens and the narrower baseline of the APS-C 70D's AF sensor. With f/4 lenses and a third party 2X TC I have had more (limited) success regarding AF using one of my FF bodies than using an APS-C body with the same lens/TC combo. But since the 70D won't recognize the lens at all I highly doubt that is the issue.

That's the risk you take buying third party lenses, though. It may be that you are experiencing what is often the downside of using an older third party lens on a newer camera body: AF incompatibility. Lens makers such as Tokina do not license technology from camera makers such as Canon to insure compatibility. Instead they reverse engineer the technology in order to design compatible lenses. When a manufacturer such as Canon then introduces a newer model that was not available when the third party lens was designed they can make subtle changes in the protocol that renders the older third party lens incompatible.