Pokemon Alpha Sapphire and Pokemon Omega Ruby retains some of Pokemon X and Pokemon Y innovative features like O-powers, Shot-outs, Holo Caster, and some online features, battle system, Pokedex and overall game presentation. Since Pokemon OR/AS introduced new moves, abilities, items, and Mega Evolutions, there are compatibility issues that will impose restrictions when it comes to trading and battling Pokemon from across the titles. Serebii has made the information about compatibility available below:
Battles
You can do anything when playing with other Pokemon OR/AS players. Restrictions will only apply if you try connecting to Pokemon X / Y players. You can't use New Mega Evolutions, moves, or items against these opponents. The game will specify what Pokemon or item you can or cannot use. The matchmaking will also somehow segregate OR/AS and X/Y players so they won't get matched up.
OR/AS League: Open only for players of Pokémon Omega Ruby & Alpha Sapphire. This league allows use of Pokémon that were caught, hatched or distributed in Pokémon X, Y, Omega Ruby & Alpha Sapphire only.
XY League: Open only for players of Pokémon X & Y. This league allows use of any Pokémon, including those that were transferred from Pokémon Black, White, Black 2 or White 2.
Battle Compatibility Chart
Trades
You cannot trade Pokemon holding new Mega Stones to Pokemon X/Y, as well as Pokemon who knows new moves. Pokemon from X/Y and other older games should transfer to your Pokemon OR/AS just fine.
Trade Compatibility Chart
Pokemon Bank is a separate downloadable application that was introduced shortly after Pokemon X and Y was released. As the name implies, it allows players to store up to 3000 Pokemon in an online repository at a cost of $4.99 annual fee (US and Canada) and download the stored Pokemon to their current-gen Pokemon titles (X/Y, OR/AS). For first-time users, the application will prompt you to purchase a Pass (good for 1 year) before you can use the service. The number of days the service is active will be displayed as well.
Before transferring, the Bank prompts players to remove their Pokemon's items so the new Mega Stones won't cause any compatibility concerns. While players can store ANY Pokemon from any version, Pokemon with new moves can't be downloaded to Pokemon X & Y. Cosplay Pikachu cannot be transferred as well.
Information provided by: Serebii.net