The British Vickers and German Maxim LMG08/15 ('Spandau' from the name of the main manufacturer) had the same basic design derived from the original model created by Hiram Maxim and first demonstrated in 1884. Both had an unrestricted rate of fire around 600 rpm, and were fed by a canvas belt containing approximately 600 rounds. The main difference between them was the design of the interrupter gear used to prevent the propeller from being hit by the machine-gun bullets.
The British designs used a hydraulic system that applied a safety catch preventing the gun from firing when the propeller was in the way, which tended to reduce the rate of fire quite significantly. However, the German design used the engine to fire the machine gun at the right moment via a series of levers, which actually increased the rate of fire slightly as it assisted in recoiling the breech block. ÂÂ
As a final note, when the first interrupter gears were fitted to the Sopwith 1 1/2 strutter, they left the original pistol grip on the Vickers machine-gun, which allowed the pilots to override the interrupter gear to increase the rate of fire - with obvious risks. The pistol grip was removed in subsequent aircraft.
Edit
'Interrupter' gear actually fall into two designs, Interrupter and Synchronizer, the former interrupting  or stopping the gun from firing, and the latter synchronizing firing with the engine. Both have strengths and weaknesses, and much depends upon the actual speed of the engine relative to the cyclical rate of the gun in question. Both sides made improvements in the rate of fire of the machine guns, while the speed of the engines are not a 'constant' depending upon what the aircraft is doing. Furthermore there were many different types of engine varying quite significantly even on the same type of aircraft. Finally, the variable quality of ammunition combined with the inherent design of the gun caused frequent jams. Veteran pilots would often insist on loading the belts themselves to reduce the incidence of jams while some also carried a wooden mallet to hit the cocking handles if any occurred.
Suffice it to say that the above views on the relative rates of fire are very generalised statements indeed.