MOBI is a legacy format without proper CSS support. Among other things, embedded fonts and dropcaps aren't supported. Also, you cannot update the cover and must instead reconvert (publishers often use pathetic generic covers instead of the real ones).
All things that were fixed in AZW3. The only reason to prefer MOBI is if you have an old Kindle that doesnt support AZW3: like, the Kindle Original/2/DX.
Even the Keyboard got a fimware update and supports it.
AZW3 has feature-parity with EPUB2+3.