Is it the engines or the fuselage that limits service ceiling?
Service ceiling is defined as the maximum altitude at which the aircraft can maintain a specified rate of climb (typically 500 feet/minute for jets).

The service ceiling is dependent on a number of design factors like,


Engine power
Engine efficiency at high altitudes
Wing design


The service ceiling is usually limited by a number of factors, and engine is important among them.


Thrust (or power) decreases with altitude (density) and at some point the aircraft reaches an altitude where even at the 'maximum rate of climb' speed, the engine will not be able to produce enough (excess) thrust to get the required rate of climb. This will be the service ceiling. Usually this is the limiting factor for GA aircraft.
In case of very powerful engines, the wings may stop producing enough lift, though this is rarely the case.
In case of transport aircraft, the service ceiling may sometimes be limited by the maximum altitude from which they can descend to 14,000 ft in less than a specified time (4 min). Commercial airliners are usually limited by this certification altitude.
In commercial airliners, the cabin pressure altitude is held constant (usually ~8000 ft ISA) and the differential pressure will cause stresses on the fuselage, but this is usually not the primary concern as fuselage design incorporates elements (for e.g. relief valves) to relieve pressure when this differential pressure goes beyond a limit.


In short, usually it is the engine, rather than the fuselage that limits the service ceiling.