It turned out that I have these two cameras for my business. First headache was to make them as compatible as possible. After several sleepless nights this is what I came up with:

These settings work for me when I set both cameras' white balance to "sun" preset.

Sony FX1 picture profile:
Color level +2
Color phase +5
Sharpness 10
Skintone DTL OFF
AE Shift 0
AGC Limit OFF
At Iris LMT F11
WB Shift 0
AWB Sens HIGH
Cinematone OFF
Cineframe OFF

Canon XH A1 preset that I named FX1 SUN
GAMMA N
KNEE H
BLACK P
MASTER PED. -9
SETUP LEVEL 6
SHARPNESS 1
H DTL FREQ H
DTL HV BAL 0
CORING 0
NR1 0
NR2 0
COLOR MAT. N
COLOR GAIN 6
COLOR PHASE 7
R GAIN -2
G GAIN -2
B GAIN -3
RG MATRIX 8
RB MATRIX -5
GR MATRIX 0
GB MATRIX 0
BR MATRIX 2
BG MATRIX 2

This seems to be working for me. If somebody comes up with some better settings to match both cameras, please share. Soon I plan to post XH A1 preset for custom white balance under the same Sony picture profile settings.

Howdy,

I also happen to own both of those cameras, although I honestly don't understand many of the XH A1 settings :)

Doesn't Color Phase rotate the "Color Wheel"? I've always thought of that as a useless concept and keep it at 0 on all cameras. Perhaps I am wrong though...

Cheers,
Anna

Yes, it does rotate. In my case, I had to rotate them to match. The biggest challenge was to match green color of these cameras.

Thanks so much for share this information. Very util for me.