I don't see too much difference between the two, although the World Cup is obviously bigger, as it involves the whole world.. It's nothing like the Champions League and the Europa league, where you have a two tiered system with the better teams in the Champions League.
Most of the world's top international teams are from Europe, and no non European side, bar Brazil and Argentina, has even played in a World cup final since 1950. So, as far as I'm concerned, the Euros are only a small step behind the World Cup.