William Wallace the semi legendary yet historical Scottish hero was defeated at the battle of Falkirk by an army led by Edward 1st himself in 1298. The Scottish nobles who comprised a large part of Wallace’s cavalry fled before an arrow was fired according to chroniclers of the time. Wallace’s schiltrons were decimated by the long bow an insight into what would befall the French some years later. However unlikely what would have happened if Wallace had been victorious?
Well, he would be probably defeated the next time because tactics he used more or less doomed him to be defeated by a competent opponent who had a big number of the archers. His schiltrons had been circular formations used strictly for the defensive allowing enemy's archers to use as much time as they needed to "soften" them enough to make vulnerable for the cavalry attacks. Compare that to Bannockburn where Bruce used his pikemen offensively. Of course, to be fair, Edward II at Bannockburn had much fewer archers than his Father at Falkirk and left them without a protection so that they had been easily routed by Scottish cavalry and English position at Bannockburn was not well suited for a cavalry. Then, again, Robert Bruce was forced to fight a pitched battle at Bannockburn: his methods of war were fast raids and scorched earth. What was Wallace' style of a warfare (when not acting as a leader of a small band) is anybody's guess: at Stirling Bridge he got all the credit because his co-commander, Moray, died almost immediately afterwards. It seems that he chose Falkirk as a battlefield intentionally and stood there for quite a while, which does not necessarily qualifies him as a good tactician or strategist: in the pitched battles the Scots would be at a definite disadvantage due to their weak cavalry.