It depends on the version you're playing. In the NES each class gets a different amount of JobEXP depending on the action and the class. I seem to recall there was a walkthrough on Gamefaqs that had them in but I can't seem to find it now.

The DS version is different; each class gains the same JobEXP for any "valid" action (anything but switching rows and attempting to run/flee), giving you 20 for all classes EXCEPT the Scholar which gives 24. However due to the way it's calculated Scholars will gain Job Levels at the same speed as the other classes. Once you reach Job Level 14+ the JobEXP per action changes depending on the class. For example Thieves get 18, while White Mages only get 10. This FAQ has the full table in it.

Generally speaking the things that your job level affects is your damage output, including physical and magical attacks. In the DS version it will also increase the effectiveness of some of your class-unique skills. The base stats are based on your character level and job selected and are not affected by your job level. Neither is your HP or MP.