Can we really call the Burj Khalifa influential when it hasn't even been around for 2 years? As for inspiring, well I guess it's a matter of personal taste but giant needle-cock buildings never did inspire me personally.
Maybe something like the Giza Pyramids, Gaudi's buildings, Taj Mahal or the Sydney Opera House would've provided a grander point of reference if you were going for that.
This could be one of the most influential and inspiring buildings in the world.
Up there with the Burj.