The original plan looked very different from what was later realized. Which was a significant driver of the cost.
Just for fun, lets compare it to the Sydney opera house:
Elbphilharmonie, original projected cost: 186 Mio EUR
Elbphilharmonie, final cost: 866 Mio EUR
So in the end, 4.65x the projected cost and 7 years late.
Sydney Opera house, original projected cost (inflation adjusted cost in parens): 7 Mio AUD (70 Mio EUR)
Sydney Opera house, final cost: 102 Mio AUD (632 Mio EUR)
So in the end: 9-14x the projected cost and 10 years late (depending on if you compare based on the inflation adjusted costs).
Therefore, in comparison, not that dissimilar.