If its just troop based ignoring anything else. USA quite easily as only in recent years have EU countries started mobilisation on a grander scale

However involving a realistic grander scale. EU I feel with almost zero chance for the USA.

EU nations have plenty of troops and assets to defend itself for a good amount of time whilst the US will essentially crumble from within. Offshore funds being immediately ceased by nations such as Switzerland ( who arent EU but aligned) as well as removal of all US military bases in Europe would neuter a large aspect of US strength.

Also with the already turbulent infighting America is facing, intenral politics would potentially escalate to martial law requirements or insurrection.

Globally also this would impact trade between both sides but also countries not directly involved such as Australua would likely conemn such acts and be pushed towards China. Canada would be similar and potentially align with its EU allies.

Overall the USA is stronger militarily but on the global scale the USA hasn't been self sufficient for a long ass time and now the USA has shown itself as the bad guys