CV machines still have some slope to the volt amper curve, but for short circut performanse another factor is inductance. The combination of the 2 governs how the short is cleared, and how much spatter You get.
AWS Welding Handbook Vol. 2 covers this to some extent.
You can see the volt amper curves of power supplies graphed in thier owners manuals. I find the Miller website the easiest to use.