Generally we do shield the signals (parallel shielding) both sides with VSS or VDD.
But, sometimes we do shielding the signal (parallel shielding) with one side VSS and other side with VDD, what are the advantages of this type of shielding ?
Your shields might be "VSS" and "VDD" but -which- VDD
(and VSS) can be a significant question. Power planes
carry switching noise if they are in the current path. A
quiet "branch" would probably be better than opportunistically
running under a logic-bed's power net.
Vdd/Vss shielding may be used when you are concerned with rise/fall times. I've had engineers request I do a layout both ways. Add some parasitic caps connected both ways and see if there is a difference.