They're not that far apart in terms of quality in terms of the specs. Miyata has a better reputation than Nishiki but both made good bikes.
AFAIK, the Miyata 610 used a lower quality steel for the fork than the rest of the frame. Personally I'd lean towards the Miyata as it should have clearance for a fatter tire than the Nishiki and I'm a fan of Miyatas. It is was one of the best Japanese bike manufacturers BITD.
That said, a good argument could be made for the Nishiki.