Hi, theoretically the Lumia Camera takes better advantage of the hardware of each Lumia.
Some sentences taken from Reddit:
"Unfortunately. The problem is that the Lumia camera probably has better access to the hardware, and therefore works better, something the Windows Camera will never have, because it muat run on all devices, not only Lumias."
"The Lumia camera app was built for Lumia phones specifically.It had extra access to Lumia firmware.Microsoft wanted all windows phone users to have the same capabilities, but that means the app has to work on all phones, not just lumias, so they had to generalize it. "
With reference to video recording without doubt the Lumia Camara is better, but with respect to the photos I do not know.