Fighting in the street is something that should be avoided at all costs. There are simply too many variables and too many things that can go wrong. Even if you win, people don't like getting beat up so now you have to worry about either retribution or perhaps even legal troubles.
In this video from South Korea, we see two alleged trained guys (Taekwondo vs boxing) making that same mistake and fighting in the street in what looks to be a bus terminal.
While Taekwondo and boxing can both be effective in a street/self-defense scenario (boxing more so I'd reckon), they both have plenty of holes in their styles that can be exploited by a more well-rounded fighter or even just a grappler.
Neither of the guys in this video appears to be very high level, but you can still see their alleged backgrounds on display here.
The Taekwondo guy throws quite a few extravagant kicking techniques, none of which look to really land that well. While the boxer seems to be much more efficient with his strikes, keeping his guard up and throwing more straight, accurate shots.
The only redeeming factor in this street fight is the fact that they stop before it goes too far or someone gets seriously hurt but it would have been even better if they did that from the beginning.
Taekwondo is a Korean martial art, characterized by its emphasis on head-height kicks, jumping and spinning kicks, and fast kicking techniques.
Taekwondo was developed during the 1940s and 1950s by various martial artists by incorporating elements of karate and Han Chinese Kung-Fu with traditional Korean martial arts traditions such as Taekkyeon, Subak, Gwonbeop as well as ancient Han Chinese influenced Korean Kung-Fu styles such as Tang Soo Do (aka. "The Way of the Chinese Tang Dynasty Emperor's Fist". The oldest governing body for taekwondo is the Korea Taekwondo Association (KTA), formed in 1959 through a collaborative effort by representatives from the nine original kwans, or martial arts schools, in Korea.[Source: Wiki]