Benefit of shielded ac wire? Any downside?

For preamp and amp.
In-wall or power cord? What are you talking about? Of course there is a downside.
I have made my own shielded power cords for decades using three conductor 12 gauge cable with a foil shield. I hook the shield up on the house side only. Does it help? I have an extremely quiet system but I can not tell how much the cords add to it. There is certainly no down side as long as you do not hook up both sides of the shield which might produce ground loop hum. There are lots of very sturdy plugs out there. I use Marinco plugs.
Sharper sounding but actually dirtier transients, combined with a subtle mushing of the dynamics.

Basically the same thing it does to all audio cables, but on the AC.

Immunity/separation/isolation from some types of noise.... with a side order of signal damage.
teo_audio said it all tec like, but that is the just of it. Different combinations of shielding can KILL the dynamics of an amp because of a "power cable". Poorly designed power supply doesn't help either along with a incorrectly shielded power cable and then use an AC filter and maintainer.  Disaster, SQ wise, if your not careful.

@teo_audio and Miller carbon. I'm speaking of the in wall wiring. Would like to be further informed. I understand? Wire acts as an antenna and thought?  10 gauge shielded wire from the breaker box to the receptacle would be a good idea. Thirsty for knowledge :)
@ mijostyn. Thanks. How/why did you decide on this?
Ptss, a very good timely question as I am building a home and will place 2 dedicated circuit for my system. I am also wondering the benefits of running shielded cables to the outlets from the main breaker box.
I recently moved to a new house. I have wired my system from the breaker panel with starquad 12 awg solid core wire direct to my distribution block. And a 10 awg , counter rotating, earth wire. Starquad has the advantage that it is a selfshielding type of geometry combined with lower inductance due to the double run.  I only use shielding on low level cabling and some digital equipment. Shielding gives blacker backgrounds, more details, but can kill the boogie factor and leads to compressing transients IMO. 
In Australia 240vac I believe it can’t be approved because it’s considered illegal and dangerous, and you wouldn’t be covered by insurance house or personal should the mains short to the shield, which would be attached to the case of your equipment also so it will become live as well.

Cheers George
... I have wired my system from the breaker panel with starquad 12 awg solid core wire direct to my distribution block. And a 10 awg , counter rotating, earth wire ...
Was this wire rated for the purpose and for in-wall use?
THe benefits:
Better rejection of EMI/RFI signals, like from routers, switches etc.
None really, though some claim the sound is duller.  I say it's because you are hearing less noise.
@cleeds . It is standard wire. I just braided it myself. It is a double run, normal wire for in wall use twisted in starquad. Pitch twist about 4 inch. It took a while for 15m. A good foundation for my system. Direct connection to my star wired distribution block, skipping wall outlets & power connectors.  

Run a 10/awg BX- cable solid core conductor from the breaker panel to a metal receptacle box. The metal sheathing on the BX-cable absorbs the (EF)) electric fields emitted by the wires and shunts it to ground. Now from panel to plug is shielded. The upside is low line noise and reduced antenna effect. Downside BX-cable is pricier. Hope that helps. Mike.  

Checking into BX it seems like the sensible option as it also protects from nails, screws and rodents.
I wonder what hi-fi companies that sell high end like Spectral, Pass, Levinson, Goldmund, FM Acoustics, Constellation - advise their clients re home wiring?
Considering that the line/neutral in BX cable is twisted which results in lower inductance versus ROMEX which is separated and parallel, I would like to hear the reasons why BX would result in mushed dynamics?

Lower inductance would make for dirtier transients, but with people pushing low inductance power cords, you need to decide if you are going to have your cake or eat it with that argument.

As cleeds is suggesting, if the wire is not intended for in wall use do not bury it in a wall. No sane electrician will do this. If the inspector catches it he could lose his license. If you do it and your insurance company catches it (after the fire) you lose everything. If you want to run special wire you can wire it to your breaker box and run it externally. It would be a bit messy but you could do it.
ptss, why do I do it this way? Because it feels good is the best answer. 
There are a lot of wires crossing paths at the equipment rack and I want to shield interconnects from AC as best as possible. Aside from keeping power cables apart from interconnects shielding adds another layer of protection. With the phono stage on and volume opened up to explosion levels all I get is a hiss which you can hear one foot away from the speakers. On the hard drive you can't hear anything even with your head in the speaker. I have not checked this out with the supplied power cables. There may not be any difference but, I've already tossed those.
The Marinco plugs are really nice and they look sharp.