The "J" in SJ refers to "Junior" or cables with 300V-rated dielectric. The "SO" without the "J" refers to 600V-rated cables with heavier jacket.
The common Neutrik NAC3FCA and NAC3FCB connectors are rated for 250VAC and 20A. To my knowledge there isn't anything specific that says you need to use SJ or SO cables with PowerCon connectors. The cable has to be of the sufficient gauge to handle the current draw. I use 12/3 SJOOW cables.
The Cliff's Notes version is that if it's on the floor, it's supposed to be SOOW: NEC 520.68A(1) Conductors for Portables "Flexible conductors, including cable extensions, used to supply portable stage equipment shall be listed extra hard usage
cords or cables." SOOW is "Extra hard usage"; SJOOW is "Junior hard usage".
The article goes on to discuss exemptions to the extra-hard service rules, but the exemptions basically boil down to cables that are physically protected (off the ground), and short (less than 6.6' on the floor/less than 20' in the air).
That said, this is one of those grey areas, as Whirlwind sells UL-listed Powercon power distribution with SJOOW jumpers:http://whirlwindusa.com/catalog/power-electrical-distribution/cables/nac3-length
(if you look at the full-res picture you can read SJOOW on the cable)http://whirlwindusa.com/catalog/power-electrical-distribution/stringers/pl1-420-wh
For additional background and reading:https://www.controlbooth.com/threads/powercon-prices.41109/