Those two hotels are literally steps away from each other. As far as getting to other areas, the transit options, ease of taxi access etc. will be the exact same. Just a matter of which hotel you prefer. I haven't stayed in either, so I can't comment.

The immediate area around the hotel will be busy during the day with office workers and fairly quiet after 9 PM. For nightlife, you can just walk east to Jongak/Jongno 3 area, Myeongdong etc.

There are several airport buses including Korean Air Limo Lines that go to that area, so in reality, you can catch one of several buses if they come earlier than the other.

Also, on the way back to maximize time, take the train. If your flight is at 2, you should be at the airport around 12-12:30. Don't want any lunchtime traffic risk.