Trout vs Koi

I'm not sure if you mean from a predator-prey perspective or water quality. Large trout (10"+) typically add small fish to their diet - and this could include koi.  Prior to achieving 10", they feed on insects, zooplankton, detritus, and other organic substances.  Large trout with small koi will definitely lead to koi being eaten. Koi are more tolerant of reduced water quality than trout.  They withstand higher water temperatures and lower dissolved oxygen levels better than rainbow trout.  Koi can also tolerate stagnant wate for longer peiods of time than rainbow trout. It would need to be just the right condition of inflowing water at the upper tolerance limits for trout in order for them to coexist in the same pond.  The bigger the waterbody - the greater the chance both species can find a niche that will suppor their needs.