Some Pokémon have had new additions to their move pools after ORAS. These are the following differences:

Ariados does not have Knock Off or Swords Dance

Banette does not learn Encore or Swords Dance

Bibarel does not have Aqua Jet and Swords Dance

Butterfree does not have Air Slash or Hurricane

Bellossom does not have Quiver Dance

Carnivine, Castform, Chimecho, Emolga, Illumise, Ledian, Servine, Swoobat, Unfezant, and Volbeat do not have access to Defog; Murkrow cannot have the combination of Prankster and Defog.

Dedenne does not have Dazzling Gleam

Dewott does not have Knock Off or Sacred Sword

Duosion does not have Stored Power

Emolga does not have Energy Ball

Glaceon does not have Calm Mind, Freeze Dry, or Icicle Spear

Glalie does not have Icicle Spear

Gothitelle and Lunatone do not have access to Nasty Plot or Stored Power; Lunatone does not have Power Gem; Gothitelle does not have Focus Blast

Gourgeist does not have Power Whip

Grotle does not have Shell Smash

Heatmor does not have Drain Punch

Hypno does not have Draining Kiss, Focus Blast, Knock Off, or Stored Power

Lopunny does not have Close Combat

Luxray does not have Agility

Noctowl does not have Hurricane or Nasty Plot

Pikachu cannot have the combination of Extreme Speed and Fake Out or Extreme Speed and Volt Tackle.

Sawsbuck does not have Headbutt

Seaking does not learn Swords Dance

Seviper does not have Gunk Shot, Knock Off, Swords Dance or Zen Headbutt

Slaking does not have Knock Off or Zen Headbutt

Solrock does not have Flare Blitz or Swords Dance

Stantler does not learn Agility and Stored Power

Sudowoodo does not have Head Smash, Iron Defense, or Spikes

Sunflora does not have Weather Ball

Swirlix does not have Sticky Web

Swoobat does not learn Nasty Plot

Walrein does not learn Swords Dance

Wartortle does not have Shell Smash

Wigglytuff does not have Draining Kiss, Nasty Plot, Stored Power, Taunt, or Zen Headbutt

Wormadam does not have Quiver Dance and Bug Buzz

Please note, this only discusses moves that exist WITHIN GENERATION 6. Moves such as Fire Lash, Trailblaze, Tera Blast, or [insert new current generation trendy move] are not mentioned because they would not be made until later generations.