Here is the problem I am having, I had a new unit installed last year on my new house. I noticed that the compressor runs for a long time and shut off for a short period. This got my attention and wondered if the unit is running efficiently. I had my doubts from the start since the A coil looked too small when it was being installed, but I decided to wait and see.
The question is, if I was to use thermocouples to measure the air temperature on the return right before the A coil and on the exit right after the A coil, what kind of differential should I expect? Please specify °F or °C units.

It depends a lot on the outside ambient temperature as well. You should see any where's from 15 to 25 degrees F deference depending on outside temperature, return air temperature and what the air flow is over the evaporator coil. You may also be low on refrigerant or the unit could be to small for the load.