Depends on what you call M.E. scale. There was no single scale reduction from the large props to the small ones. It varied be the race and sometimes the scale actor size. Sting is an odd one that falls in between the small scale actor-double prop and the large Elijah actor scale prop.
There was an old thread from 10-12 years ago here here where we talked about Sting's creation when my memory was fresher on all this stuff. I did a search, but I guess the current version of the website does not go back that far. Anyway, Sting was the first LOTR replica we made, and we had very little to work with. This was before New Line had their LOTR assets machine up and running, so all we had were some photos of various Sting props, which all looked slightly different. We did not have a length, so I had to guestimate the prop scale from photos of Eljah holding it. Remember, no one had seen the film at this point, so we really had no idea how they were going to scale the Hobbits, or how much Sting would even be seen.
We knew the Hobbits would be scaled down in the film, but no one could tell us what that scale reduction was. We had to start anyway because we had a contractual on market date to meet for UC replica, but we did eventually get lengths from NL for three prop sizes before we started on the tooling. There was a small-scale actor double prop that was around 17", a middle scale prop length of 22", and a the large Elijah scale. I can't remember now, but I think that was 27 or 28". There was a big discussion at UC about which scale to make, and we picked the middle one. We were eventually loaned a prop. I think it was the middle scale, but I don't remember for sure now. I'm pretty sure we had already started tooling by then anyway, so it was useless at that point. Much later Weta sent me the small-scale actor double prop, but we were already on the market by then. Then the film comes out and we mostly see the Elijah scale prop on screen, which is proportionately different from what we made. That's what sparked the idea for the more screen accurate MC Sting a few years later.
Anyway, sorry for the novel. I guess the short answer is "neither".
Here are some of the Weta prop photos we were given. I think the bottom two were all we had to work with when we started.