From the Shadow Dragon template, it would appear that the Shadow Breath has the same damage and save as the original dragon's breath weapon, as no change is stated in the template:
New Action: Shadow Breath. Any damage-dealing breath weapon possessed by the dragon deals necrotic damage instead of its original damage type. A humanoid reduced to 0 hit points by this damage dies, and an undead shadow rises from its corpse and acts immediately after the dragon in the initiative count. The shadow is under the dragon's control.
However, analyzing the provided example of applying the template to a Young Red Dragon (whose Breath Weapon has a DC of 17), the Young Red Shadow Dragon has a Shadow Breath with DC 18.
Am I missing something? If the DC was kept at 17, would it lead to a different CR? In that case, what comes first: The CR or the DC?