No overlap between any two Core Class specs coming from multiple sources.
If they came from the same class, then obviously some things can be shared.
And the New Spec of the Echo Class could be flexible enough to share abilities with any/both Core specs, given that it fits the overall theme of the spec.
Example:
Spellbreaker has Protection (Paladin), Arcane (Mage) and Spellblade (New Spec).
Protection has all of the abilities of Prot Paladins pertaining the spec and its effectiveness in combat. All abilities visually get adapted to an Arcane blue/purple sparkle. The goal is to maintain balance, therefore it retains all the (shitty) Heal spells, the Blessings, and more. The resource mechanics are also the same; Mana and Holy Power (renamed Arcane Power). Blessings, while carried over, will be self-only buffs instead of Party buffs. Out of Combat abilities like Ressurection can be completely omitted. Divine Shield can be delegated as Prot-only, not Class-wide. None of these abilities will cross over into Arcane spec at all.
Arcane has all the abilities of Arcane Mage pertaining to the spec and its effectiveness in combat. You have all your Mage Armor, Spellsteals, Counterspells intact. Intelligence Buff will be only castable on Self, no longer castable on Party members. Portals and Mage Food/Drinks can be omitted, since they are Out of Combat abilities. Time Warp could be changed to a Self-only cooldown ability rather than Raid buff, while allowing it to remain a party-wide effect for Arenas. Visually, this spec can equip Shields alongside a Sword as an Echo Class perk. None of these abilities cross over into Prot spec.
Spellblade will be the new spec. Since it is new, it can be designed to be anything that helps define a Spellbreaker's identity and gameplay. For the sake of example, we can consider it a Melee DPS spec with mid-long range abilities. To push the Spellbreaker identity, this Melee DPS spec allows 1H + Shield combat, differentiating it from other 'Magical melee' classes. The use of Arcane magic continues as a theme between all specs. Spellblades can be designed to incorporate certain abilities or cooldowns from other specs. Say for this example, a Spellblade spec has access to Divine Shield and Timewarp, making them very effective survivalists and DPS. In this particualr design, Spellblade spec does not carry over other abilities like Lay on Hands or Mirror Image. Those would remain specific to Paladins and Mages as class-wide abilities.
Spellblade would be able to pick and keep whatever suits the gameplay. Spellsteal and Control Magic? Avengers Shield? Sure, lets keep em. Evocation? Holy Light? Not so much. And of course, on top of all that, the Spellblade spec will have its own gameplay designed for itself: Arcane Strike, Mana Fissure, Feedback, Disruption, Spellglaive Storm, etc.
And as a class overall, we can adjust the Class Buffs and Raid Utility where it fits. Sure, this class will lose out on the utility of bringing Blessings or Intel Buffs and Timewarp to the raid, but what you gain instead is a Spellbreaker who has its own brand of Utility and Raid Buffs. We could implement a Moonkin Spell-crit aura that ONLY* affects party members. So in a raid setting, there's going to be plenty of buff overlap where bringing a Spellbreaker isn't going to make a huge difference, but you still have reason to have Spellbreaker, Paladin and Mage in the same Dungeon party.