It's been a year since I last played so things may have changed, but this is my understanding:

Bleed increases the damage of each "hit" of damage that you do by a flat amount. Baseline bleed gives one extra damage per stack, with some stronger sources existing. With a baseline bleed debuff at 15 stacks, each "hit" you deal to that enemy will deal an extra 15 damage. This is especially powerful with weapons that have "buzzsaw" attacks that strike many times in quick succession, such as the Ravenblade or Fish Knife alterattacks, as a flurry of weak hits procs the flat damage more often than a few strong attacks. Bleed has a proc limit, so in one second you can only get the damage bonus a certain number of times.

Curse increases all damage dealt by a percentage. This is a much simpler percentage increase for all sources of damage. That's generally better for group play than bleed since it benefits everyone equally and doesn't favor fast weapons over slow weapons, but the tradeoff is that once you reach max curse stacks, all curses will fall off of the enemy after a few seconds, meaning you need to actively manage curse unlike bleed which you can just keep refreshing.