The reason the Tutors are on the G- reg is because they where one of the first examples of this government's Private Finance Initiatives, the planes are not property of the RAF (or the crown) simply on long term lease (this makes them much easier to get rid of when the RAF has finished with them)
Methinks you are confusing 2 issues. DHFS helicopters are civil owned and military registered (COMR) as (now) are the King Airs. Just because they are leased does not mean they have to be on the civil register. Unfortunately being on the civil register means you have to operate them to all civilian rules, as an example you cannot fly the Tutor with miniflares fitted in your LSJ.
Back to the original question, IMHO the Tutor is just the better aircraft. Better avionics fit than the Bulldog, better climb performance with the 3 bladed prop (as long as all three blades remain attached
) better flick ability (and who cares that this has no military application) but less forgiving undercarriage, lower x-wind limit and a m u c h s l o w e r roll rate. Horses for courses really, but I think the Bulldog was more fun!!