Community Manager Zarhym had this to say on the subject on Thursday afternoon:
.@lordreinhart @cm_zarhym Yes, pet battles are rewarding more XP than intended right now. We're testing a hotfix to address this asap. :) - World of Warcraft (@Warcraft) March 7, 2013
The XP scales with your level and how close your pets are to the pets you defeat. XP is earned via battling pets in the wild, pet tamer NPCs, and other players in pet battle PvP. No experience is gained from pet battle duels or if your highest pet is more than 5 levels above the pets you are fighting. The amount received before the nerf was roughly what a character gets from completing the capital city cooking and fishing dailies.
Because you can get XP from battling level 1 wild pets, people were camping out in major cities and decimating the battle pet population while leveling their low level pets.
As of this morning, it looks like all realms have been hotfixed so that the experience is approximately 10% of what it was. We have no further official word on the nerf as of this writing, but we'll keep you posted.
Update: It looks like from the comments and my experimentation that the nerf is scaled. While it is no longer worth it to hang around Stormwind and kill level 1 pets, if you battle in level appropriate zones with level appropriate characters, the XP gain is still worthwhile.