I want to know which is a safer mode of transportation for students
ages 14-16 traveling for three hours to a camp site complete with
equipment for a weeks stay:
a 10 year old school bus with lap belts only, three kids to a seat and
all equipment stowed in the aisles OR a new motor coach with
upholstered seats, no seat belts, 2 to a seat, toilet facilities and
all equipment stowed underneath in baggage compartment.

The new one.  Less likely to break down, more confortable, provide
cleaner-than-public restrooms, no stopping and letting all the kids
out at a shady, dirty gas station.  The seatbelts are the only real
difference, but are far outweighed by the benefits that the newer
coach provides.  The new vehicle would probably perform better in a
crash anyway, they tend to be more stable than the standard yellow
schoolbus.  If you give specific types of vehicles, more research
could be done.

chicagomt asked for more specific info on this subject. School bus in
question is standard yellow about ten years old, three to a seat, lap
belts only. Not a state of the art vehicle; although perfectly safe
for local neighborhood school transports.
The motor coach (as exemplified by the ones used previously) are a
state of the art; excellently maintained by a reputable company. The
only lack here is the lack of belts.
The trip is 2 hours on an high speed interstate to the camping destination.