Presumably it "has" to work that way otherwise somebody flying into the USA would not be able to.
The really big differences are in VFR flight. Europena pilots just cannot believe that in the USA one can fly VFR up to 17999ft (Class A base is 18000ft) and gets easy transits through most controlled airspace, etc. Class D transits are with just 2-way radio contact (no explicit clearance needed).
A US pilot (IR holder) who does an IFR flight in Europe will first hit the Eurocontrol routing system. After he has found a way through that, the flight is pretty well as he might expect. He does need to stick to reasonably high levels for it to work; in the USA this is formalised in the way the airway MEAs are shown on the chart but in Europe this is more vague.
The fun bit is if he cancels IFR; then he needs to know the airspace, and all the other stuff.