Whose OD is a better match for an early Sherman?
Tamiya's or Model Masters?

I have only used MM OD for my US WWII builds. IMHO it seems the closest match. I have used Tamiya's OD for post WWII vehicles as the color is quite a buit darker. However, in the field, the troops used whatever green they could get their hands on. This is still the same premise in modern warfare. You use whatever color you can find.
There are a couple of exceptions to this. They are the USAF and the USN. They can be a little more specific due to abundance of supplies.

I will second Matt, I only use MM Olive Drab. I use the Acrylic and airbrush it, but I find MM makes the closest OD.