Not as much as people think.
If you are within a day's walk of help your first aid need only be very basic.
A large sterile field dressing is arguably unnecessary as the wound is far from sterile before it goes on.
A clean sock, scarf or torn off bit of cloth is ample to press on the wound. When you get to A+E, the wound will be properly cleaned before closure.
I also stopped carrying sachets of saline/antiseptic on the same basis. Wound/ eye irrigation can be done with boiled water from my canteen in the field before A+E do it properly.
For any sizeable wound problem you need way more irrigation than you would carry in a first aid kit. I like the idea of the burns pack if you are away from water, but that's rarely the case in this part of the world.
I carry:
Plasters, alcohol wipes and gaffa tape for blisters, small cuts and splintage.
Scalpel blades and sterile needles for blisters, splinters, nail haematomas (and possible heroics)
The drugs I carry are limited to minor ailments or lifesaving.
Painkillers
Antihistamines
Antacids
Antidiarrhoea
Aspirin
Pottasium permanganate (quick decontamination of lots of water)
I think that's it, I'll check it to see if I've forgotten anything. It all fits in the side pocket of my small possibles pouch.
Of course for a multi-day trip, this changes completely depending on the environment.