I played Alan Wake on Nightmare difficulty off the bat and had good fun with the combat. Playing on Nightmare gives combat that extra oomph that keeps you on your toes.
While finding standard ammo still isn't really a problem (which is one of my beefs with the game), enemies hit very hard and take notably less damage from both guns and flashlight, so you really need to keep aware of your surroundings and be more tactical in how you take them out. Dodging becomes absolutely crucial and in some cases the best tactic is take a couple out, duck under other enemy blows, and just haul ass to the nearest light source as your wheezing Alan Wake is being chased mercilessly. Gives it a bit of that extra survival horror flavor.
I thought it all worked together beautifully with the general ominous atmosphere the game sets so well. Every time the screen got dark and the inky shadows surrounding you started to dance and waver, you knew that it was on, and every pool of light from a car or lamppost was heaven-sent (a similar feeling in some ways to getting to a bonfire your first time through Dark Souls).
What I would have preferred in Nightmare difficulty is for ammo to be more scarce, so that it'd lean even more towards survival horror, but you still hardly feel like some superman.
I've never actually played Alan Wake below Nightmare difficulty so I don't have a concrete basis for comparison, but I imagine it's naturally just more prone to feeling repetitive when there's no real tension to the fights and you're just going through the motions.