Mostly I only really need my EXP card when using a BA lounge, as they have a policy of not believing what's printed on your BP and will often only admit you with the card. (See threads passim in the AA forum - though I've never understood - if they think you could fake your status on the BP, why should they believe you're flying at all? Surely you could fake the whole thing.)
Never flashed my HH Diamond, though maybe I should after the crappy service I've had at a couple of properties, notably the SEATAC Hilton and the ES CLE - contrasted with the last time I stayed at the Hilton Newcastle. The client called to make my booking and was told "Oh yes, Mr chartreuse, he's a Diamond member!" Upgrade, lounge, everything. Way to become one of my favourite properties