difficulty vs dilemma

difficulty

noun
  • An awkward situation or quarrel. 

  • Physical danger from the environment, especially with risk of drowning 

  • An obstacle that hinders achievement of a goal. 

  • The state of being difficult, or hard to do. 

  • An objection. 

  • That which cannot be easily understood or believed. 

dilemma

noun
  • A difficult circumstance or problem. 

  • A type of syllogism of the form "if A is true then B is true; if C is true then D is true; either A or C is true; therefore either B or D is true". 

  • A circumstance in which a choice must be made between two or more alternatives that seem equally undesirable. 

  • Offering to an opponent a choice between two (equally unfavorable) alternatives. 

How often have the words difficulty and dilemma occurred in a corpus of books? (source: Google Ngram Viewer )