My experience is that damage healed by first aid is proportional to damage taken, more or less.
At high levels, a trap that does 40 hp damage may get 20 hp back on First Aid.
I have even seen low levels of poisoning be more than counteracted by First Aid - does 1 hp damage, recovers 2 hp.
First aid utility is also based on what your current PV is. If a character has 2 PV, every bat and goblin pecks away at your hp. First aid will keep you alive.
With a PV of 20, what gets through is either magic, penetrating, or overwhelming damage.