Rod1, you have clearly already made up your mind on this one!
Your two scenarios don't really bear comparison to me. In scenario one, provided you are already in receipt of a BS, the controller/FISO
already knows your details. This will include a/c type and last reported position and level. Even if you haven't made a specific position report for a few minutes, the controller is quite capable of working out where you are to within a few miles. Additionally, we'll also (assuming we've had a call from them) know of other a/c in the area who can go and have a look for you, and who has the time to provide us with a more specific location. I have yet to speak to a pilot who won't help out a fellow aviator in this situation.
In scenario two, you may have to provide
all your details to D&D in that one Mayday call. Especially as, at 1500ft, it is unlikely you will manage a full triangulation from D&D.
I know what I'd choose!