It would depend if both boards has the LEDs wired the same or not.
Are the board’s LEDs common cathode or common anode?
The rest of the board being common ground or not would not effect how the LEDs are wired.
So pay attention how the LEDs are wired and where their polarity is going.
LED diagram here for reference
The Mad Catz Xbox 360 TE player indicator lights, as well as the PS360+ and the Brooks Universal Fight Board are all wired for Common Anode.
Which they would be like this on the TE guide PCB.
As for your Xbox One Mini controller, I can’t say. You need to apply voltage to each LED on the board to find the polarity, and probe around with a multimeter to see if the board’s LEDs are common anode or Common cathode.
I got a question to other people who are more Electronic Engineering inclined than me, assuming there is a controller PCB which lights are Common Cathode, is there away to make this work with another board which lights are set for common anode? Hex inverter perhaps?