Whenever I am given the option to choose a difficulty in new games I tend to choose "easy". The reason I tend to do this is that the majority of the time the game is absolutely no different except you tend to do more damage while the bad guys tend to do less. It really bothers me when games do this and ruins the entire point of a difficulty selection. However there are games out there that use the difficulty selection as actual game play. My favorite examples of this are Wolfenstein 3D and Doom.
When you picked a difficulty setting it would either add or remove enemies to maps. So the designer was designing the experience. These gave way to awesome gameplay experiences and replay ability. Maybe on one difficulty setting you could run right through a room but on the next difficulty setting maybe there were two or three bad guys in the room ready to ambush you. Plus the enemies actual difficulty was still the same you were just dealing with more difficult situations. So you could actually build up your skill as a player. I would love to see more examples of this in modern games, and maybe there are and I just haven't seen them. Too many games come out to keep track of or really spend time with so I am sure there are gems out there. If you have any hidden gems of this example let me know I would love to check them out!