Running a dedicated A/C circuit

I am curious to learn if there is additional benefit in running BX as opposed to Romex because of the armoured spiral alloy wrap. Is there an inherent shielding factor that the Romex lacks or any other improvements in controlling resonance etc?? Thanks.
I would avoid introducing any ferrous materials into your circuits.
Aluminum, zinc, copper and brass are non magnetic.
Stainless steel, if non magnetic, is also good.
That includes boxes, connectors, screws and raceway.
BX has been replaced by MC cable, I won't go into the differences.
If you must use MC, specify aluminum, instead of steel clad.
I am not a fan of shielding everything, it can choke dynamics to death.
On the other hand, I am constantly experimenting with resonance damping. (DIY quartz products)
When you hit on it correctly you can hear the improvement.
Over do it and you'll shut the dynamics down.
Mrderrick, Try using Amethyst crystals. Get them small and unprocessed. I bought a pound on Ebay for $10 including shipping.
Place small amounts in the plastic baggy things and tape the bag over your Circuit breakers to your system or on top of power cables.

I even wash the crystals in sea salt for 8 hours then rinse with 90% or better alcohol and let dry in the sun.

It may take a few weeks too sound good but when it does the dyanmics will improve and so will the overall sound quality. With the baggies you can experiment how much to use.
I just obtained some mini Amethyst in bulk.
There was a "bulk" amount of black Tourmaline powder on Ebay, but it was way more than I wanted to purchase.
Supposedly, it is used in therapeutic baths.
Type MC cable is an alternative to BX cable (a.k.a. type AC cable) but has not necessarily "replaced" it. BX cable is still actively used in some areas. Also, some jurisdictions do not permit plastic boxes or non-metallic cable. In such locations, you have the option of aluminum armored cable or rigid conduit but will have no choice but to use steel receptacle boxes. It is always wise to check local codes.