Gangnam is too broad for one route
A hotel near Gangnam Station, COEX, Jamsil or another south-side district can have a different useful bus stop and rail transfer. Start with the exact address and count the final walk; a page that says only ‘take the bus to Gangnam’ is incomplete.
Rail is a network route
Neither the AREX Express endpoint nor the all-stop airport railway is the final Gangnam destination. A rail plan needs a transfer and station movement. It may still suit a budget traveller with light luggage, but it should be compared door to door rather than by the first train segment.
Groups and luggage strengthen the taxi case
A taxi does not become cheap automatically, but several travellers can share its fixed inconvenience and avoid multiple changes. Use the official Seoul taxi framework and a live estimate, then compare that total with each person’s public-transport fare and the value of the transfer removed.