Little Joe Mth of Weaver?

I have both, here are my thoughts. There are several things to consider. First is which remote control system you prefer. The Weaver unit has TMCC, the MTH is DCS. Next, the rooftop detail. The Weaver is detailed for a passenger engine, the MTH for freight. I don't know which roof detail the South Shore units had; you'll have to find a photo from above to check that. Then, there is the question of the nose angle. The Little Joes originally had a long, sloping nose similar to an E-6. One of the Milwaukee Road's freight units was wrecked and the cabs were rebuilt with parts from EMD. As a result, the nose on that one unit slopes at a steeper angle, more like an F unit but not quite the same. The MTH nose is at a steeper angle than the Weaver, suggesting that they took that angle from a drawing of the rebuilt unit. However, the MTH Joe is not a complete model of the rebuilt one, as the rebuilt unit had EMD side grilles and the MTH has the original style.  For a South Shore unit, presumably the Weaver would have the correct nose angle. 

Finally, there is the question of operation. The MTH unit is a smoother-running unit with better low-speed performance. The Weaver has an old K-Line cruise control board in it; if you replace the cruise with an ERR unit, the low-speed performance of the Weaver should be just as good as MTH. Also, the MTH may have automatic pantographs. I can't remember for sure and mine is packed away at the moment. Automatic pans are a mixed blessing. They are cool when they go up and down automatically when you change direction. On the other hand, the MTH mechanisms are notoriously unreliable and when they get out of adjustment they are a pain to fix. 

Here are two photos. The orange and black one is MTH, the maroon, orange and black one is Weaver. The first photo compares the nose angle; the second compares the roof detail.