I can't really make out what you have as a rear derailleur on the Miyata, but on the Nishiki, it looks like a Suntour ARx, which is okay, but not the best Suntour has to offer. If you can find a Cyclone, Vx, V-GT, or BL, give one of those a try. I have a Cyclone on one bike with a modern ramped cassette, Suntour Symmetric shifters, and cheap cables/housing, and shifting has always been crisp, light, and precise. Also be sure to check droupout and derailleur hanger alignment. As a comparison, I had an older Suntour GT matched with a Suntour freewheel on a different bike, and while it was reliable, it always needed overshifting.