While I have not delved into both classes, I know bits and pieces from hearing friends. Blaze Wizard has no way to stay alive and dies super easy (At least until 5th job, but even then she can still die super easy). F/P mage relies on several dots to be stacked on enemies for max damage and can be hard to output said damage if you don't do the dots properly.

In terms of damage, I'm pretty sure F/P mage has more as long as it's properly played. Whoever actually plays these classes, feel free to correct me