PowerPSoC has additional power peripherals like hysteretic controllers, CSA etc in addition to the core (which is same as the PSoC 1 core - M8C). Indeally, it should be possible to port the code to a PSoC 1 device but you will have to use external components.
The key advantage of Cypress' solution is that it is is a single chip solution for battery charging and driving LEDs. PowerPSoC has 4 channels of the power peripherals, these can be used for LED driving as well. So, with one PowerPSoC device you can implement a single chip solution for charging the battery and driving LEDs.
You can find all the details about the Cypress's MPPT solution at the link - http://www.cypress.com/?rid=72393&source=header.
The Application Note that Dana mentioned has all the details about this solution along with the firmware. The AN link is http://www.cypress.com/?rID=39126