In general the two different arts are very similar. Both use kicks, punches and blocks. One of the main differences that i have found with Taekwondo is the stances are more narrow than Karate stances. The focus is on forward and reverse movement. Karate stances are wider and more balanced. They emphasis is on movement in all directions. As attackers can come from any and every direction, I believe that Karate stances are superior. In all reality the difference can be a litttle as moving your foot inward and turning the toes to a different direction. Almost as if the origins of these martial arts are next door neighbors.
Another major difference is in the kicking. Taekwondo uses kicks very similar to those used in karate, but i have found that Taekwondo has basic kicks..... front kick, back kick, side kick and turning kick. there really is no intermediate kicking techniques. They jump straight from these basics to jumping and spinning versions. If you haven't been training for a century or two and are not an overly athletic person then these spins and jumping kicks are extremely difficult to use. With Karate you have numerous kicks that are what i would term intrmediate. These kicks are reasonably easy to pull off and can inflict huge damage. Hook kick, inside or outside straight leg kick, knee kick, kicks to the knees, these are examples of intermediate kicks. One major that i have found isthat karate has a roundhouse kick. Usually when you use this you either hit the opponent with the top of the foot or you pull the toes back at the same time as hooking your foot back toward you shin.
In Taekwondo, you only use the later. This limits the distance that can be reached when performing the kick. To compnsate, Taekwondo fighters would either jump or spin to try and distract the opponent. As you may have guess by now. I believe Karate to be superior. Everything Taekwondo has.... karate does too and more.
There are literally lots of different variations of these martial arts it really depends on the person to person basis so its very difficult to answer your question.
This may interest you Jerome http://uk.eurosport.yahoo.com/blogs/world-of-sport/article/69139/
Chelsea FC - UFC is a BRAND, not a martial art. There are many fighters in there who practice both Karate, Taekwondo and others.
But to answer your question Jerome; There is no 'best martial art', only good martial artists.
But, having said that. Taekwon-do is split into two dominant factions, Olympic Taekwondo and True Taekwon-do.
True Taekwon-do practises on the fundamental and more dangerous aspect of the sport, using strikes to end a fight as quick as possible. This is the same version pioneered by the great General Choi Hong Hi in April 1955.
Some disputes led to the breakaway and formation of the WTF (World Taekwondo Federation) and the ITF (International Taekwon-do Federation).
Unfortunately, the leader of the WTF was also a leading IOC member in Asia, and pulled strings to have it included in the Olympic games. But the ITF (the style i have practiced for over 10 years), is the original and superior martial art. The Taekwondo you see on the television is fake, useless and relies purely on entertainment...
As for Karate, well, again... There are many styles, Shotokon, Wado Ryu, Kenpo, Kyukushin etc... ut again, there are no dominant styles.
As for boxing. Well put it this way, my legs are longer than your arms, and i have NEVER lost to a boxer when i've been allowed to use my leg attacks.