The lead mode on the red stripe Mark III is closest to the IIC+ lead which is what Metallica used. Just about any Mark III will get you reasonably close though. My blue stripe does a fine job at it. Just make sure to get one with the 5-band EQ built in.
If you really want that scooped album sound, you are going to need an EQ in the fx loop as well, even if your amp has the 5-band EQ. A parametric EQ was used on the albums but any decent EQ pedal or rack-mount unit should work. I have a Boss GE7 pedal and I can get about 95% there with it. Also, Flemming Rasmussen posted pics of his notes from the Puppets / Justice recording sessions that you can download and use as a guide. They are for the IIC+, but very easy to adapt to the III.
As for which of the Mark III's have a "better" tone, that's all subjective. I don't even know that there is a huge tonal difference between the various stripes. I mean, I can't imagine it would night and day, just minor tonal variances.