Only kill XP is shared between players. Other XP gain, such as the various Awards (as listed in Blem's answer) that you can earn at the end of a map, are individually earned and thus can cause this discrepancy. Some of them are flat bonuses, like Knight and Lord, but others, like Invincible (for not taking any damage after the first wave) and Gunslinger (only using weapons and abilities after the first wave) are multipliers (1.3x for those 2 in particular, last time I knew). The values of the flat bonuses vary based on difficulty and map.
For instance, as I was leveling my DPS Huntress, I was able to keep up in experience levels (and sometimes, even outlevel) my other 3 companions because I consistently received the Gunslinger award, giving me 1.3x to my score.
If your Apprentice is using only towers, whereas he is using a mix of towers and character DPS, you may be getting the Master Strategist (used only defenses to harm all enemies after the first wave), consistently, which while it is a flat bonus, really adds up over time. In addition, if you're hanging back and not taking any damage during a wave, whereas he is in melee and getting hit, you may also be getting the No Player Damage (not taking any additional damage during the wave), which is another 1.3x multiplier.