Well, I'm not sure if there is much of a difference from a level 30 knight and a level 5 knight. But one penalty for not keeping the same class (for mages anyway), is spell effectiveness.

Before I found out that changing jobs to make sure everyone has a nice magic defense was pretty much useless, I found out that my white mage (level 30ish), was healing more with a regular cure than a level one white mage. (The difference was around 100-200 hp). for 30 levels, thats probably not saying much, but maybe if I used something like curaja, there would be a bigger difference.

Also, for spellcasters, the higher job level means more spell casting.

For fighters, I'm not sure but maybe the higher the job level, the more times they swing their weapon? I had a viking that swung his weapon around 10 durring their attack. (yes, i switched this one to be a mage). Then, with my original white mage, I changed him into a viking. (not really neccesary to say, but at the time, vikings had better weapons for me). This new guy only swung his weapon around 5 times per turn.