I'd recommend iems (closedbacks at this price point are hopeless) for when you have to be considerate - they're not gonna be quite the same, but its your best option - then use the hd6xxs when you dont have to be :D
Although i'd say maybe listen softer - hd6xx shouldnt leak enough sound to be a big problem at sane listening volumes
Honestly, I'd say if you have the opportunity to try higher-end gear - try it, and arrive at that conclusion yourself :) That's the fun of this hobby - discovery, no?