When you come and dive with us in Key West, we require you have A certification card with you. The standard spiel is that you sign the waiver and hold us not liable for anything basically. That being said, I suggest carrying just your AOW card unless you are going to a dive operation that has varying skill level dives, like the Vandenberg.
The problem with showing a DM or OWSI card is that now you are identified as a "thought to be proficient and competant" diver who might be paired up with a noob or someone who the crew feels needs babysitting. As stated earlier again, you might need to do a rescue 10 mins into your dive.
I dont want people to know that I teach. I dont want people to know I dive trimix when I go to the boats unless I am specifically there to dive that type of dive. People see my gear and ASSUME I know what I am doing because I have tec equipment, a nice bag, and a well worn wetsuit I dive in. But I have also seen novice divers hauling "seasoned vets" back to the dive boat who presented a DM or higher card, yet had not dove in YEARS!!! One diver admitted he had not been in the water in over 10 years, be he had his OWSI card. He had his ass handed to him on a platter by Davy Jones that day almost immediately upon entering the water.
So pick and choose what to take, and take what you feel is the maximum you will need. If you are doing a wreck like the Vandenberg, take your wreck, deep, and nitrox cards. We as dive operators appreciate knowing who we dont have to watch, babysit, and anticipate a rescue for.
Just please leave the underwater basket weaving card at home......