One runs at a lower resolution, looks worse, and only has access to one analog stick on the PSP. The other looks pretty and shiny on the Vita, and adds touchscreen control as well as a second analog stock. But both are the same price?
Lord of Apocalypse, the sequel to Lord of Arcana, will hit the market with two separate versions, but they're priced the same for Japan. Siliconera says that the retail of 5,980 yen ($77) is for either a UMD disc or PlayStation Vita card.
Other than the resolution and input types, we're not sure what's different between the two versions. While it may not look as good, the PSP version is more versatile, as it will play on both your PSP and Vita systems.