Same waterproof and layered system, but expect more walking and rougher ground. South Georgia and the Falklands can be windy, wet, muddy and uneven, with longer hikes than a typical Peninsula landing. Reliable traction, calf-high socks, proper waterproof pants and a daypack all matter more here.
Some Falklands visits include towns, farms or longer walks where comfortable waterproof hiking shoes are more useful than tall landing boots. Your operator will tell you when expedition boots are required and when your own walking shoes are appropriate. Check whether supplied boots even cover these landings, since that varies.
Biosecurity is at its strictest on itineraries moving between the sub-Antarctic islands and Antarctica, because you're preventing transfer between sites, not just into the region. Clean pockets, Velcro, bags, poles and footwear exactly as instructed.
Pack layers flexible enough to handle a warm walk and a cold exposed Zodiac transfer on the same day.