What are the differences between the difficulty levels in BioShock Infinite?

I've played on both Normal and 1999 mode (one notch above Hard) and I can say that:

• Enemies are more accurate, and do more damage. They have more health. Their weaknesses and critical regions are the same.
• The quantity of "cannon fodder" weak enemies is hard to quantify, but if it has increased, it is not significantly so. All other encounters that I've seen have the same composition of the harder enemies, in the same quantities. Based on my experiences, I want to say that the quantity and type of enemies per encounter is fixed.
• Loot quantity and quality is hard to quantify, as the loot is randomized every time you load a checkpoint, even. From my sampling, I believe it to be similar across difficulties. I still find 80% health kits on downed enemies, and large quantities of money in lootable objects, for instance.
• Stealth is unchanged. Turrets and other automated defenses will react the same way, and the instances where you can choose to be low profile are completely the same.
• The AI's behavior is completely the same. I'm employing the same tactics in my 1999 run as I am on Normal, and there's nothing that they are doing differently.

There are a couple of things you didn't note that did change, however:

• The shield recharge delay is massively increased, and the recharge speed is considerably slower. This essentially means crowd control and cover are both essential.
• It doesn't feel like my "companion" is helping as much. She still tosses me things, but the delay between assistance seems longer.
• This might be considered "loot drop" related, but it seems like the amount of ammo I gain from picking up a weapon in the world (either a fixed spawn, or from a downed enemy) is less. There are a couple of rooms with racks of weapons, and I feel like on Normal I walked out with a fully maxed out weapon, and on 1999 I barely have half the max amount of ammo.