The big concern for SK is right next to its north, and THAAD is an overkill for its safety, PAC-3 and others are just adequate for that purpose. THAAD is not for SK, it is for U.S. and Japan because of its long range radar which none of the other systems (PAC-3) has.
Coz altitudes, speed, trajectory of different BM actually necessary have in general one ABM for each type/range of BM and it is the problem.
THAAD range of 200+ km is capable intercept BM with a max range of 3000 km in US Army Battery of 6 TELs, she have right now 3 soon 5 units.
Patriot Pac-3 range 20 km last variant 35 km is capable intercept BM owith a range of 1100 km max.
So THAAD have a ABM range 5 to 10 times superior and vs more big missiles.
A Patriot Battery sometimes designated company have in general 6/8 TEL if equiped with 2 variants about 1/4 to 1/3 of TEL with Pac-3 coz he is quadpacked and one TEL can have 16 Pac-3 against 4 Pac-2 much less capable vs BM, a little but have a long range 160 km vs aircrafts.
For this reasons, differences all Services which have two variants have mixed units.
US Army Batalions of 24 TEL in 4 Battery, 2 Bat of 35 ADA Brigade are stationed in SK, one other Bat to Kadena
But SK have 48 Pac-2 former Germans in 6 batteries and have ordered kits for modernization with Pac-3 missiles.