@HardWater, VBAT and WKP play different roles. The VBAT pin is meant to keep the RTC running and to preserve backup registers and some (4KB) of SRAM when VDD drops. This comes in handy during power loss or when VDD is purposely dropped by an on/off circuit for example. The VDD (drop) event can trigger an interrupt so that the STM32 can react prior to a switch to VBAT. So, essentially, VBAT is a way to preserve key data while power is turned off.
The WKUP pin plays a role in the low power modes (stop, standby) of the STM32. Unlike STOP mode, the processor cannot be awakened using an external interrupt while in STANDBY mode. The only way to do this is using a rising edge on the WKUP pin. Remember that STANDBY mode provides the lowest power consumption short of dropping VDD.
On the Core, there is no access to the WKUP pin so the RTC, external or IWDG resets need to be used to exit the STANDBY mode.
The Photon will support a non-reset STOP mode, meaning the code will actually stop predictably until an external interrupt event wakes it. Because of the IDWG, the Core must force a reset to properly get into STOP mode. For a lower power state where your code can handle a RESET event, you will be able to use the WKUP pin to wake the Photon from STANDBY mode.
I hope this helps! 