Chromium accounts for almost all of the rust-resistance, and nickel (needed in very high amounts) to some small degree. O1 has very small amounts of each (chromium 0.4-0.6%, nickel 0.3%); not huge by any means, but it might make just a teeny-tiny bit of difference in rust-resistance. 1095 has no chromium or nickel in the alloy, at all.
Having said that, neither steel has anywhere near enough chromium to even approach 'stainless' status (needs 12-13% or more), so the small difference between them might be moot anyway. I don't think I'd base a buying decision between these steels on rust-resistance alone. That's probably a very minor difference anyway.