While looking for the answer, I discovered there is a whole Wikipedia page about the subject. It quotes the conclusion of a NASA study "Non-nuclear kinetic impactors are the most mature approach [...]" (2/5) en.wikipedia.org/wiki/Asteroid_…
But if you look closer at this study, you'll find a graph that clearly shows that nuclear bomb is way more efficient than a projectile. (3/5)
However NASA said "mature" and not efficient, indeed this same study mentions "because of restrictions found in [...] Principles Governing the Activities of States in [...] Outer Space, use of a nuclear device would likely require prior international coordination." (4/5)
So yes, Michel Bay was right, nuclear bomb is the way to do it 💥 However deflecting an innocuous asteroid to improve the science about this subject was probably not convincing enough to get an international approval to send a nuclear bomb into space. (5/5)