The best western gunfighters shot from behind, or shot when someone wasn’t expecting a fight. The gunfight near the OK corral was fought at very close range, and it is likely the Earps drew first - which is always an advantage. That, and many of the shots taken missed.
Notably, Ike Clanton had been publicly stating his intention to kill Wyatt Earp. He and his companions were also carrying guns in violation of a town ordinance. The Earps were law enforcement officers, with Holliday deputized and part of a legally authorized posse to disarm the Clantons and McLaurys. The best view of the evidence is that the initial gunshots were mutual and virtually instantaneous.
Although the Earps and Holliday were cleared of criminal charges, like many cops versus criminals shootings today, the issue was not fully settled as a matter of debate. Moreover, the gunfight also had political aspects that carried over into contemporaneous accounts and later histories.
In essence, the Earps, with the qualified exception of Georgia native Doc Holliday, were law and order Republicans from Iowa aligned with the leading Republican businessmen and townspeople in Tombstone. The Clantons, McLaurys, and the Cowboy faction were mostly Democrats of Southern origin allied with like-minded townspeople, ranchers, criminals, and cowboys in the nearby rural area.
Initially, public opinion rallied behind the Earps, but a determined campaign by the Clantons and McLaurys and their supporters made the issue a close one despite the Earps and Holliday being cleared of criminal charges. In the 1930s, Left-wing Western writers and historians began to shade the facts so as to call into doubt the correctness of the conduct of the Earps and Holliday. Over the last twenty years though, most histories have tended to favor them, with Judge Spicer's ruling and the rediscovered trial transcript making for strong support in their favor.
You are of course correct about most Western shootings being more in the nature of bushwhacking than straight up open gunfights. Tom Horn's notorious career bears that out, as do many instances in which there is nothing to go on but the body of someone shot dead in unknown circumstances. The record of the era is that it was usually the outlaws who did the back shooting, not the lawmen. Many of them took great risk to bring law and order to the West -- and I count the Earps among them.
Also one thing Earp had over the Cowboys in a bar fight or shootout was Earp did not drink. He was sober.