Using differential and single-ended inputs simultaneously in a data acquisition system
If you tie the shield to ground at the ADC you will unbalance the impedances of each side of the differential input and be more susceptible to common mode noise, and also create a ground loop. You should rely on the ground from the sensor end.







simulate this circuit &ndash; Schematic created using CircuitLab

Some additional power/decoupling capacitors at the sensor would not hurt if the supply cables are lengthy. 

By the way, the BNC model may not be the best choice for 10m.