Yes and no. What you're not comsidering is the obligation of The US Federal Reserve (aka The Fed). While dollars are international, The Fed's only concern is the US and US citizens. That is, often enough The Fed makes decisions that achieve this ends, but screws the rest of the world. Such decisions become self-serving to the USA's power, influence, etc. That decision undermines other countries, economies, etc.
So yeah, the USD is stabler, and The Fed helps to see to that.