The main structure of the European Union is based on the fact that a crisis in a single country can lead to serious financial consequences throughout the euro area. In the USA there are no such banks that are completely dependent on the financial situation that is observed in a separate state.
Therefore, the answer is obvious - the dollar is more reliable.
There are mechanisms to prevent a single country's misdeeds from bringing down the European Union. There are rules around how much a country can spend, how much its fiscal deficit can be, etc. With the USA, there are no rules - the President is in charge and he may boost the dollar or run it to the ground. With Trump in charge, I am not sure that the dollar is the more reliable bet.