[JonA]

Originally Posted by Lesman

Which way is more 'correct'

Well, neither method is more correct. The only true measures are of usability, controllability and accuracy. You can look at all sorts of data and generate all sorts of graphs and you could probably choose variations on algorithms that allow the most control and accuracy at a given range of speeds. In the end, it comes down to "does it do what you need it to do?"

Here is one easy way to look at it:

Usability is usually subjective. This includes how complicated it is for the driver to drive and, perhaps, how complicated it is for the programmers to write.

Controllability is closely tied to usability but focuses more on consistency. (ie: when I put the stick in this position, will it do the same thing?)

Accuracy is more objective and measurable. (ie: when I put my stick at 45 degrees, does the robot travel at 45 degrees?)

Originally Posted by Lesman

...sliding at a 45 degree angle at full magnitude is not full forward + full sideways, as that would result in root(2) magnitude (on a scale of -1 to 1) in that direction, which is obviously not possible.

In the end, for controllability and usability, it is usually best to limit the maximum speed in any heading to be the same. Just because you can you can drive faster in the forward direction as opposed to 45 degrees does not mean you should as when you start to turn, your speed is not proportional.