Well, first question is why those two in particular.
Truth is I'm a bit agnostic. I like the L6 type steels- when done right they are really tough. I also love working 1084. It's a good steel for hardening and tempering, and can be tough enough for throwers and hard enough to satisfy most anyone. I'd go with O1 just because I've worked it more than A2, but any of them will do the job.
I'd go with 5160 or L6 for a big chopper rather than thicken the blade of something more brittle, but truth is as I said, a high carbon straight steel like 1084 can be made tough enough for the work.
For a smaller sheath blade, like a nessie or bushcrafter or whatnot, anything that will harden will work, really. Sometimes steel choice depends on preferred geometry, too. I like the L6 type for a convex edge, but a stiff scandi works fantastic in o1
All of this is personal opinion. I'm NOT the most experienced maker out there, and I haven't worked with every steel enough to know everything. And a lot of this is based on personal experience and preference.
BEtween the two you listed, O1.