You may love strategy, but maybe you want to stick to coaching at the head coach level and leave details to your offensive and defensive coordinators. You might choose Beginner difficulty because it’s a nice balance between coaching and simulating, but without all the complexity, or maybe you want to play a more relaxed, faster game.
First, let’s look at the difference on offense. In Expert, you can tap any player, in addition to the Head Coach icon. When you tap a player, you can designate him as the ball carrier, assign him to block, change his pass pattern, etc.
In Beginner, however, you simply tap the QB or Head Coach and call a type of play, leaving the details to your offensive coordinator.
Here’s how the initial screens look:
Hard Core – notice more players are tappable

Now look at the menu options in Casual difficulty. No formation or other details, just call your type of play.

By comparison, Expert has lots more options (Formation, designate receiver, choose drop back vs play action, set a man to block, etc), but is also more complex:

Defense is similar. In Expert, you manage the focus, formation, line shift, everything. In Beginner difficulty, you know you want to defend middle runs, or short passes, etc, and you let your defensive coordinator manage the details.

