Hi,
The answer is that EyeTV 250 is appropriate for game systems, and TVMax is not.
The hardware encoder in EyeTV 250 can be disabled, which eliminates the latency, but as a trade-off increases CPU load.
The hardware encoder in TVMax cannot be disabled, making it unsuitable for games because the latency will be about 1 second.
The advantage to a TVMax is having the inputs mounted on the device rather than on a break-out cable and having the ability to encode DivX and MPEG-4, which EyeTV 250 lacks. Neither of those help you with respect to video game systems.