There are 5 different loot boxes in Versus.
SUPPLY BOX is available in the main menu and unlocks automatically every 4 hours. New unlock starts only after you claim the loot.
COMMON BOX is a regular box, that you get by winning battles. Time to unlock - 3 hours.
RARE BOX is a better version of common boxes. They also drop new gears. They can be earned by winning battles or purchased in the game shop. Time to unlock - 8 hours.
EPIC BOX is super rare and give even better rewards than common and rare boxes. Contain epic cards. Received by winning battles, also available in the game shop. Time to unlock - 12 hours.
PREMIUM BOX is only available in the game shop and unlocks instantly. It contains the best loot in game. May even drop a new character!
NOTE: All the boxes, purchased from the shop, are unlocked instantly.