疲劳 is more formal than 累 (lèi). Use 累 in everyday speech ('I'm tired') and 疲劳 in written or medical contexts (疲劳症 'fatigue syndrome', 疲劳驾驶 'fatigued driving').
memory
Both characters share the idea of exhaustion: 疲 (skin stretched thin from the illness radical 疒) + 劳 (labor). Skin worn thin from labor = fatigue.
