Originally Posted by Roger

King's Cross to LCY is 35-37 minutes station to station, changing at Bank. LCY is adjacent to the terminal, just steps away.

King's Cross to LHR T5 is 43-49 minutes station to station, changing at Paddington (and sometimes also at Edgware Road) using the HEX, whose station is more than a few steps away from check in. Alternatively about an hour nonstop on the Underground.

If you're using public transport, LCY offers a shorter and IMO easier journey.

Info from http://journeyplanner.tfl.gov.uk