Both are quality flutes. However, I think you may have some misinformation about the Muramatsu EX III. It has a Sterling silver handcut headjoint and a silver plated body. It is also considered a handmade flute. Quoted from the Muramatsu website:
The EX model is our most economical flute, yet it offers the same high quality Muramatsu workmanship you will find on our higher priced models. The hand-cut, solid silver headjoint on this attractive instrument is carefully cut and matched to a silver clad body and key mechanism, the same reliable key mechanism used on our most expensive flutes.
I have played a Muramatsu AD for 20 years and it is a very well made flute. I play a lot of different flutes because I also repair them. The Azumi is also a fine flute. Why not try both and compare them? If you are buying online, get both on a trial. Most reputable flute stores will ship you 2-4 flutes to try for a week.