The Spad XIII was a great aircraft. Its top speed was significantly faster than the other fighters of the day. The aircraft was also significantly heavier and with a much more powerful engine than other fighters. In that way, the Spad XIII is a bit like the equivalent of a World War I P-47 but with the speed of the Me-262 and the production numbers of the Me-109. But it still appears that the Spad was outclassed by at least one or two aircraft in dogfights.
"Starting Line" - Eddie Rickenbacker in Saints by Russell Smith
This painting entitled "Starting Line" is of Eddie Rickenbacker in Old #1 about to take off on a sortie while he was in Saints. Russ writes that "most depictions of S'4523 show it in its late configuration - shortened exhaust stacks, red/white/blue (front to back) rudder, and patched bullet holes. However during its time at Saints - circa August 1918 - S'4523 carried the standard length exhaust, no bullet patches (at least not in August of 1918) and the original blue/white/red French rudder."
The Americans switched over from Nieuport 28s to the Spad XIII while in the village of Saints, just after Quentin Roosevelt was killed.
"By August 8th, 1918, our whole Squadron was fitted out with the machines which we had so long coveted. The delight of the pilots can be imagined. In the meantime we had lost a number of pilots on the flimsy Nieuports, not by reason of their breaking up in air but because the pilots who handled them feared to put them into essential maneuvers which they were unable to stand. Consequently our pilots on Nieuports could not always obtain a favorable position over an enemy nor safely escape from a dangerous situation. The Spads were staunch and strong and could easily outdive the Nieuports."
Related Links: Nieuport 28 | Spad VII | Spad XIII | Fokker D.VII and other German aircraft | Fokker Dr.1 | Albatros D.Va | What was the first American fighter plane?