Experience Points

Experience points (short XP) are a measurement for how your character is progressing. The player character can earn experience points for killing creatures and solving quests. They are used to determine when a character should gain a new level. Different amounts of experience points are awarded for killing more dangerous creatures. For example, in Fallout 3, killing a deathclaw will get you 50 experience points while killing a radroach will give you 1 experience point. Experience points can also be gained for disarming mines and traps, picking locks, hacking computers, passing speech challenges and occasionally doing sections of a quest.

Fallout 3 difficulty modifier
Changing the difficulty level will also change experience gained from killing enemies. On Very Hard you will receive 150% of the regular experience for a kill, while a kill on Very Easy will only yield 50%. For example, a Deathclaw is worth 25 XP on Very Easy, 50XP on Normal and 75XP on Very Hard.

While this means that you can gain up to three times as much experience from fights on Very Hard compared to Very Easy, this is somewhat compensated by the enemies being much tougher. In the end, it depends on the player´s skills and play style which difficulty setting allows for faster leveling. Some people play on very easy until their enemy is about to die and then change the difficulty to very hard and finish them off to get the XP amount from being on the very hard difficulty.