I opened the BBF Pro manual and searched for balanced...

Page 8 in terms of AN 1/2:

The back of the unit has the XLR inputs and outputs of channels 1/2.
[...]
The Babyface Pro has two analog microphone inputs that can operate as line inputs with levels
up to +19 dBu, when set to 0 dB gain and PAD active. The electronic input stage uses a
servo balanced design which handles unbalanced and balanced signals correctly, automatically
adjusting the level reference.

!! When using unbalanced cables with the XLR inputs pin 3 of the XLR jack should be connected
!! to ground. Otherwise noise may occur, caused by the unconnected negative input of
!! the balanced input.

Page 78
AD, Microphone/Line 1-2
Input: XLR, electronically balanced
Input impedance balanced: 2 kOhm, 5.2 kOhm with PAD
Input impedance unbalanced: 1 kOhm, 2.6 kOhm with PAD
Signal to Noise ratio (SNR): 113 dB RMS unweighted, 116 dBA
Frequency response @ 44.1 kHz, -0.1 dB: 18 Hz – 20.8 kHz
Frequency response @ 96 kHz, -0.5 dB: 7 Hz – 45.8 kHz
Frequency response @ 192 kHz, -1 dB: 5 Hz – 92 kHz
With PAD active : -0.1 dB 8 Hz, -0.5 dB < 4 Hz, -1 dB < 3 Hz
THD: < -110 dB, < 0.00032 %
THD+N: < -104 dB, < 0.00063 %
THD @ 30 dB Gain: < -107 dB, < 0.0004 %
THD+N @ 30 dB Gain: < -100 dB, < 0.001 %
Channel separation: > 110 dB
Gain range: -11 dB up to +65 dB
Maximum input level XLR, Gain 0 dB: +8 dBu, PAD +19 dBu
Maximum input level XLR, Gain 65 dB: -57 dBu, PAD -46 dBu

I would use a balanced connection.