I don't know about the ammo situation where you are located, but the LGS around here are finally getting 223 ammo in. Today my LGS had PMC, TULA, and Hornady TAP ammo in 223Rem. He does have a two box limit on the number of boxes you can buy. Personally, I think it's a good temporary policy, it stops the hoarders, and resellers.
If you can get 223 ammo easily, I would have to go with the 223, but otherwise, the .357 is the better choice. You can shoot 38Spec/.357Mag out of it, this allows you to use either caliber, when the other one isn't available. This versatility is something to consider with the ammo situation the way it is. If you choose to ream it to 357Max, you have an additional caliber that you can use in your rifle.