The real difference is that the US or European countries are borrowing in their own currency and under their own laws (well for euro area countries, sort of). So they will inflate their debt away. EM countries typically borrow in USD and often under foreign law and don't have the option to inflate away.
But Greece found itself with effectively a foreign currency debt (EUR which they don't control) and ended up defaulting (well, technically "restructuring" but that's the same).