It didn't end great for the people in Czechia either.

that's not the point, the point is that spirit of both slavic people is completely different

Moscovia was shaped by the rules established during the terror of Mongol invasion, we see the effects to this day

It's hard to say if the Grand Duchy of Muscovy was shaped more by Mongol politics or by Byzantian ones, to be honest, but they certainly imitated Constantinople (or how they perceived it, anyway) more so than Sarai.