The photon has cloud compatibility and wifi access. The Arduino doesn't without a separate shield.
A photon about 1/4 the size of an Arduino UNO
Photon is much cheaper than arduinos
Arduino UNO advantages:
Arduino UNO has 5 volt AND 3.3 volt while Photon has only 3.3 volt
Arduino has many resources while Photons don't since Photons are fairly new
Arduinos don't need any wifi to work while Photons need to be connected to wifi and the cloud to flash code (Although there is a way to flash over USB cable, it is HIGHLY complicated with need of the terminal and DFU-UTIL installed.)
UNO has 5 analog, 13 digital ports while Photon has only 5 analog, 7 digital
UNOs have female pins, so no breadboards are necessary for small, simple projects.
Photons have male pins, and they need to be plugged into a breadboard or soldered.
Personally, I have both an UNO and a photon. Photons are useful for small and more compact projects, while Arduinos are for projects on a bigger scale. Unless you specifically need access to the cloud or access to WIFI, I would suggest buying the Arduino. Good luck!