Statwise, Liepard is better in terms of both offenses by a larger margin, while Persian boasts only slightly better speed and Defenses.
Persian's lacking offensive presence is made up by its access to Technician, which boosts any moves whose power is 60 or below by a factor of 1.5x. Unfortunately, Persian must rely on it's lower Special Attack for Technician, as only Fake Out and Fury Swipes are the few Physical moves that are useful to Persian with Technician (maybe except something like Aerial Ace). Knock Off and U-turn are also useful moves, but do not get boosted by Technician. It does have Nasty Plot to increase its Special Attack. However, Persian must rely on Life Orb for even decent damage output.
Liepard has a great ability in Prankster, allowing it to support the team through Thunder Wave, Encore, Weather, and more. In addition, it has access to STAB Knock Off, providing team support and dealing decent damage to the opponent. Liepard also has access to moves such as Play Rough, Gunk Shot, and Grass Knot, providing coverage for its weaknesses. Liepard can also get priority on Attacking moves through the use of Copycat.
Liepard, although less bulky, is better through its coverage and ability to provide team support.