Video Game Logic - Changing difficulty mid-game

Bestheda: Oh you haven't tried Legendary Difficulty yet?
Skyrim Nexus: Oh you haven't tried Dragon Combat Overhaul yet?
loverslab: Oh you haven't tried our B********y Animations Pack yet?

Enemies don't adjust. Your damage adjusts. Novice makes you do double damage and recieve only half, while master makes the opposite – you do half, and enemies strike double time. Legendary pumps it up further – you do 25% and enemies do 300%.
Those settings are adjustable any time and have no effect on actual stats.

Armor skills are easier to develop on novice, since the fact of a hit gives you more exp than a damage bonus, and damage skills like weapons and destruction are better farmed on legendary.