Pokémon Champions keeps the Pokémon battle rules we know, with a few adjustments designed for competition. Here is what changes, and what you need to master for your first online battles.

Single Battle and Double Battle

Single BattleDouble Battle
Pokémon in playOne on each sideTwo on each side
AppealDirect duels, reading your opponentSynergies, protection, spread moves
Where to play itRanked, friendly and private battlesThe same modes, and the World Championships format
Before a battle, you choose one of your saved Battle Teams. On the selection screen, you see the opposing team and choose the Pokémon you will send into battle. Since Update 1.2, the selection aid displays useful data on this screen.
Choosing moves in battle.
A battle in the Arena.
Selection in a private battle.

Mega Evolution and the Omni Ring

Heroes wear an Omni Ring, the equivalent of the Mega Ring from previous games. It lets a Pokémon holding its Mega Stone Mega Evolve, once per battle. The official site states that other powers could be added to the Omni Ring: Z-Moves, Dynamax or Terastallization are not ruled out for future regulations.

The current regulations allow 81 Mega Evolutions, many of which received a brand-new ability. See Mega Evolutions.

The Omni Ring.

Rebalanced Status Conditions

Champions modifies three status conditions to limit the role of luck. It is not known whether these changes will carry over to the main games.
StatusBefore (main games)In Pokémon Champions
Freeze20% chance to thaw each turn, with no limit.25% chance to thaw on each attack attempt, thaw guaranteed on the third turn.
Paralysis25% chance of being unable to move, Speed halved.12.5% chance of being unable to move, Speed still halved.
SleepLasts two to four turns.33% chance of waking up on the second turn, waking guaranteed on the third.

According to Serebii.

Level, Stats and Balancing

Battles are played at level 50, as in official competitions: the stats displayed in training correspond to that level. Several moves have been rebalanced (power, accuracy, PP), and a few Pokémon lost access to certain moves with Update 1.2. See Modified Moves.

Recent Additions

AdditionPurpose
Battle history (Update 1.2)Review the actions taken during the current battle.
Selection aid (Update 1.2)Display battle data on the Pokémon selection screen.
Disconnection penaltiesIn online competition, a disconnection counts as a loss.