The purpose of the shield is to provide a low impedance path for common mode noise to some low impedance relative to the stray coupling impedance. Considering E and I fields can be several orders of magnitude above the signal, this impedance ratio is critical for radiated noise.
Meanwile conducted ground noise is a big unknown depending on the application and proximity of SMPS line filters and ground surges and environmental RF noise.
The problem with connecting shields at both ends depends on ground currents between the two grounds and thus the induced CM current along the shield is the amplitude of the ground current. This often only problematic near large AC-DC power supplies or systems that use Y caps to filter CM noise to earth ground or if there is a ground fault with leakage to ground. It can also be problematic with near RF AM transmitters.
There is no general solution. Here are some variations in shielding;
For EEG signals the shield is often driven with the signal common mode voltage called active shielding because a stray E-field of 100V/m is 140dB above a signal of 10uV.
If the noise spectrum is RF from SW transmitters and SMPS radiated noise, the shield can act as an antenna and pre-amp input non-linearities for CM signals can get rectified producing baseband modulation noise, so RF CM chokes are used for microphones and DC power charger cords, and earth grounding is only on the AC frame. For mobiles or laptops there is no earth ground unless connected to a VGA monitor or some earth grounded audio port.
For ethernet signals the Common mode impedance is usually coupled to earth ground by 1nF caps to avoid AC ground currents going between end-points on earth grounded PC's. These always also include CM chokes to raise the CM impedance so that the differential impedance can attenuate CM noise.
Where the noise can be largest near the sensor such as in an automotive petrol engine with spark plug noise or a difference in ground noise between end-points, the shield to frame is often only connected at the source and not at the received end to avoid frame ground noise conducting thru the shield.
Below showing that common mode noise can come from the SMPS so CM choke is needed. ( same is true for Laptop chargers but shield is only earth grounded at one end. ) N.B.
- connect yellow gnd drain wire as an option
- if no ground current expected to reduce radiated noise
- or if environmental radiated noise is too high.
- but may increase conducted noise if SMPS is earth grounded on output
if ground impedances are low and gnd noise current is high.
simulate this circuit – Schematic created using CircuitLab
In this case strain gauge connectors are earth grounded thru the connector body to chassis sensors, and the internal ground path ought to be short to the power cable so this provides a decent shield for the signals. The option to connect the yellow shield drain wire at the AC ground destination depends on the difference in ground noise between the source and destination. This is hard to determine without testing or knowing the stray noise in the installation. One has to know how to test and measure noise by simulating nearby noise with solenoids or relay coils pulsing on long wires nearby. Then you can assess radiated noise effectiveness. For conducted ground noise, other tests are used for susceptibility simulation.
So there is no general answer to what is best for your application, but at least you have the option to terminate the shield at both ends or add a large Ferrite core or torroid donut or ferrite clamshell depending on the amplitude and spectrum of local interference. This is a routine design consideration for EMC for both ingress in this case and egress for PWM bridge controlled steppers.