I think most people will say Vault is harder, but only because Crota is currently being cheesed to hell and back and Deathsinger is usually skipped. The 2nd checkpoint in Crota is easily as difficult as Confluxes, and Crota requires extreme timing whereas Atheon was just more about brute force and damage avoidance. What I don't like about the difficulty of Crota is that success relies almost entirely on the sword user. Everyone else helps, but it's his leadership and ability that the entire encounter relies on. You could say the same of the relic holder, but there was some degree of randomness to that after they patched it.

The Vault IMO is more difficult. But, in the sense that it has more parts to it/more that you have to do. It takes longer even if you're 31's blazing through. The new raid is.. Kind of disappointing. But still enjoyable.