Please allow me to look at the situation from what I imagine might be the perspective of ATC. I have never done the job - I'm not clever enough - so I will no doubt get it wrong, but please bear with me.
a. An aircraft calls me, and says he is declaring an emergency.
b. Ah, he has an emergency, says I to myself. Adrenalin begins to flow a wee bit. What is the nature of the emergency, I wonder, and I ask him the question. He duly proceeds to describe his problem(s), possibly in fine detail, and in technical terms. While he is doing this, I am trying to translate into terms I understand the severity of his situation. I have a problem here, in that although I am fully qualified ATC, with a few hours on my PPL, I am relatively new in the job, and I am the only controller on duty. I also have a couple of personal problems, but they're - well - personal. (There could be the problem with the common language as well, etc. etc. but let's not go OTT.) The point is, I know my job, and I assume he knows his, but I do not know his, and he does not know mine.
c. Anyway, I'm not absolutely sure I fully understand his situation, but there is one fact of which I am quite certain: it is not as serious as all that. How do I know that? Because the pilot has not used the word Mayday. Simple.
d. The conversation may or may not continue, and no doubt I would alert at least some of the emergency services at some stage or other.
e. It is even possible that eventually I will realise he is actually in distress, and go onto full alert with the Aircraft in Distress procedure, but this is by no means certain.
Even if paragraph e. occurs, everything from the start of paragraph b. has been time wasted, for the simple reason that the pilot did not say the word Mayday. I fail to understand the reluctance of so many pilots to use that word.
As to declaring Pan Pan first, and then perhaps upgrading to Mayday, I would suggest it is safer to do the reverse. If there is an emergency, ask yourself, "Is this a distress situation?" If the immediate answer is "NO," then perhaps declare Pan Pan. If the answer is "Yes", or "Well, maybe", or "Er..." or anything else, then I can see only one thing to do, and one word to say.
I am not advocating calling Mayday every time an amber light flashes. I advocate being professional, and acting in the best interests of your passengers and those on the ground. Life is difficult enough; why make it more so for no good reason?
With sincere apologies to all you ATC types. I am trying to get across to the pilots what I consider to be a very important message, understand?