World Cup, because there is no Brazil in Euro Euro, because there is no China/Saudi Arabia in Euro Euro. World Cup is too diluted.
They are somewhat different. Qualifying is easier for the World Cup. And Euro has no easy matches. However, you have one extra round to win in the World Cup, which decreases chances of an underdog winning (we have seen dark horses capture '92 and '04 Euro, but never a World Cup). Overall, I would say it's easier to do "well" in a World Cup (by well, I define quaterfinal, for example), but it's harder to win the World Cup. It's easier to get out of the group in the World Cup and you can get lucky in 1/8 final at the World Cup and squeeze through, but it's a tougher road to the Pinnacle. Back when Euro was 8 teams, and semis-only playoffs. that was a killer tournament (just to qualify was an honor).