They're two different games, can't really compare. I'd say LV1 runs are less frustrating than Souls games though, if you die in a LV1 run you don't need to go through an entire level to fight the boss again.
I agree with FFxStrife, after beating Bloodborne the first time a few weeks back and comparing that experience to the KH LV1 runs, they are different games.
You don`t have to travel long to distances to bosses in KH like you sometimes have to do in Bloodborne. Also KH Lv1 runs rely heavily on the use of i-frames, and Bloodborne really did not have that. It makes the way you approach combat different. It`s kinda hard to explain, it`s something one has to experience.
Also like LV1 run implies, you don`t level up at all, unlike you in souls games normally. Because of that, I felt like there were more instances in the KH LV1 runs where normal enemies and bosses would kill you with one hit.