Mouse
As a opposed to a "half emergency" or a "little bit of an emergency" or an "almost full emergency"?
This has been done to death before.
In the UK (and Guy is ex UK) it relates to the LEVEL of response that ATC will expect from the RFFS.
For example if you declare 50% or more of a power plant failure to ATC we will declare a "full emergency"
This will inevitably have the Fire services(possibly from outside the airfield also) rolling to the RVP's. The local hospitals and police will activate a disaster plan (already planned for and in place) .
If you steely eyed sky gods avoid the school and bus full of nuns and disabled kids and land safely

(ie most of the time),everyone goes home. If you don't...they've gotten there a wee bit quicker.
As someone above said the cost is the same no matter what!.
Pan Pan is probably not as well recognised outside the UK. Mayday WILL concentrate the controllers mind. In the UK (at least in my little bit) it would not be unreasonable for the controller to offload other traffic to a colleague and thus keep the frequency clear for the aircraft with the problem.
Years ago I remember an old ex RAF controller/ Lanc pilot reffering to a Pan call as "ashtray full in flight".
Hope this helps.