The enemies generally take more shots to go down, and they have better aim. You can take less hits before you go down. Frequently there are scripted sequences where you have to move up in order to stop enemy spawns, so you'll have to move quickly once you down the enemies in a room in order to stop them from spawning.
There's no difference in their AI or the quantity (aside from it being more difficult to stop the infinite spawns) from what I can tell.
I play for the achievements, so I always finish the game on Veteran, but it isn't difficult so much as it's frustrating. Often times you won't have time to stick your head out before they've almost completely killed you. Get used to the death and loading screens, because even if you're epic in multiplayer, they're still going to kill you often.
I'll leave you with a few tips on strategy. There are two types of situations you will be in. The first is "kill x guys to proceed" and the second is "push the enemies back to proceed." The game doesn't give you any indication of which situation you're in, but you can determine which it is by shooting a few of the guys in a room. If, a few seconds later, they're replaced with more guys in the same position, you're in the "push them back" mode. It's certainly the harder of the two to deal with.
Strategies for pushing back:
- Sprint into the next area before they get to their scripted cover locations. Usually the AI will wait until it's in cover before shooting at you, so you can skip rooms entirely if you can get to the next "trigger point" in the hall/room before they get into position.
- Run from cover to cover, and take a step around a corner and then step back. Sometimes the scripted locations are very close to your cover spot, so you can actually cause the enemies to fall back (or your allies to push up) by moving up a tiny bit and then moving back into cover. Your allies are usually invulnerable and have infinite ammo, so they're much more effective than you are.
- Look for dead zones and alternate routes - Sometimes you can hide under objects, or find a path through an otherwise "dead" area in the map to avoid the areas where enemies spawn. You'll often end up behind them or making a large amount of progress very easily this way.
- Slot a fresh mag and fire as you come out of cover. The AI will usually try to hide if you're shooting at them, so you can force them into cover if you're shooting constantly. If your weapon has a short magazine or fires quickly, fire in short bursts so that it lasts longer.
- Use tac grenades. This is often better than if you could headshot 5 guys at once, since by the time you've killed guy #5, guy #1 is probably respawning or very close to doing so. You can throw grenades over cover, so you aren't risking yourself, and they cause a large area of enemies to become stunned for a few seconds. Use this time to move up and get them to fall back. Since tactical grenades are limited, this is usually a "last resort" strategy.
I suppose in general you should not be focused on trying to kill them. Even if you manage to snap aim and kill all half dozen of the guys in a room, you're still not going to be fast enough to move up without more spawning. Add to that the fact that they spend 80% of their time in cover usually, and you're just asking for frustration.