Honestly, it depends.
A plate boosts Arceus's STAB moves by 20% and changes Judgement's type, while a Z-crystal does what a Z-crystal does. Both change Arceus's type to whatever type the item corresponds to.
For normal Arceus form, a Z-crystal is pretty useless, as normal Arceus almost always plays the role of support or Extreme Killer. In both cases, Arceus is better off holding Leftovers or a Chople berry.
For most Arceus forms, a Z-crystal is worse than a plate, as the plate also boosts Judgement's power, giving it consistency rather than a nuke. Also, in most cases, these Arceuses (Arceii?) fit in teams which have a better Z-move user. These include Arceus-fairy, Arceus-electric, Arceus-ghost and Arceus-dark.
For others, a Z-crystal is quite useful, as it allows Arceus to decimate would-be checks after setting up. A Z-crystal is only to be used if your Arceus is a set-up Sweeper, with Swords Dance or Calm Mind. For example, Arceus-ground's boosted Z-Earthquake finishes Groudon-P and Xerneas, while Arceus-Flying's boosted Z-Fly finishes bulky Yveltal, Groudon and other checks.
It all depends on what you want your Arceus to do.