How well do you think the world and feel of the dark souls universe would translate into a tabletop roleplaying game and, further question, which system would you use to run it if you were going to try?
I wouldn't say so. If the system provides enough balance and tactical depth you could translate it quite well, even if you still have RNG giving yourself an edge through superior strategy is what keeps many TT wargames interesting. Unfortunately i don't know too many medieval fantasy systems, so I can't tell you one that delivers this.
Pathfinder is a bit to skewed concerning class balance, and the ridiculous powers that high level full casters get don't exactly help getting the feel across either.
It wouldn't really translate well. Dark Souls rewards skill and the use of the correct strategy against each opponent, which is kind of the antithesis of combat that is largely resolved via a random number generator like dice.
I'm not a particular fan of that system (I had a bad experience with it :p), nor am I familiar with Dark Souls, but Burning Wheel sounds like it might fit the bill. While there's a random element, combat is more based around outsmarting your opponent and figuring out his weaknesses, than on rolling dice.
Warhammer Fantasy Roleplay, first or second editions not familiar with third, might capture the grim setting well.