I went with a dex build and was using both bleed and poison, bandit knives with poison, and to be honest I think it was pretty weak. The upside is pretty much no boss that I've fought is immune to poison or bleed, unlike previous games. Mytha is obviously not a boss you want to poison, but other than that everything could be poisonned. That said I got the smith fairly late for the poison stones so I didn't do every boss with this setup(specifically I didn't do the fat guy in the poison area with it to see if he was also immune). In terms of damage though, they were both pretty low. Bleed is capped at 200dmg max because it's % based off the life of the mob but that'd be broken for bosses I guess, still 200 is a shit value for a cap considering it takes 6 to 8 hits to proc on anything and poison damage I'm not entirely sure how it calculates but it seemed to do 15 per tick regardless of the mob and duration looked to be about 30secs, and it LOOKED like the ticks were faster with mytha's bent blade than with bandit knives so maybe the DPS is based on the speed of the ticks instead of their value. Regardless though, it wasn't high damage, and aside from that bandit knives +10 hit for like 2 to 10 on most bosses due to armor and shit, so it's basically more or less entirely about those procs.
You could use non shitty daggers to apply the procs, I haven't tested enough but for example the rapier that applies poison didn't seem to apply it any faster than bandit knives. The manslayer katana also didn't, it looked like about 6hits for poison, even though it's about twice as slow as a dagger.
So the only advantage to dex I'd see is if you do use a poison stone on a slower weapon, you'll get some damage bonus, on bosses, but not that much. You're probably better off using a raw stone on a dex weapon or an elemental one and get damage all the time. I don't even know how useful the poison stat is either, it's hard to tell, but you could probably use a poison stone on a str weapon and get similar results even without the dex bonus, so yeah. I think bleed bonus from dex should also increase the cap of bleed procs, as for poison I'm still unclear on the exact mechanics of what poison bonus does.