Kirk Hammet has always played a black Mirage (otherwise known as "M" series) that eventually became a signature artist model. So on the ESP side as well as the LTD side, all M series and KH series should all be Extra Thin U countour necks. As far as radius, I would assume they are also the same. I'd guess 12 or 14 inch non-compound.
So all that being said, the KH-602 and the M-1000 should be the same. If it was my choice, I'd take the M-1000. Partly because it's sadly better looking than the real ESP equivalent M-II, and also, because if I ever get a KH it will be an ESP and not an LTD. In short, it all comes down to aesthetics.