Whether difficulty levels work or not is very subject to the actual gameplay.
Some examples:
Metal Gear Solid 3 is a stealth action survivor game. Playing on normal is fun; a good mix between all elements allow excellent pacing. However, the harder modes throw these off balance. For some reasons the guards acquire super eyesight, forcing you to slowly crawl through every area, completely disrupting the pace and feel. I don't feel like a smooth spy anymore. I felt more like a snail.
HAWX has a ridiculously flawed hard mode. What I expect in a combat flight game is improved enemy skill when I up the difficulty level. Instead, they change nothing about the AI and just cut down half your ammo and equipment. The "hard part" is that the player can get stuck without ammo somewhere halfway through a mission, but this is for the wrong reason. It should not be because of a number being cut, but because of enemies better dodging.
Going back to MGS3, a cut on ammo and available equipment works very well in harder difficulties because of the survival part of the game. Ran out of ammo? Throw a snake to poison guards. Battery for your radar ran out? Good luck finding another one. That should be the extra challenge, not a snail-impersonation contest.
I like games best when they have 1 difficulty level that is delicately curved out so even returners still get challenged, (coughDark Soulscough) but some games (like SSX3) fail horribly in this.