The argument about which is more important for martial arts; speed or power, is one that has gone on for centuries. It is an argument that has created very different martial arts styles. Some like Tae Kwon Do rely on speed while other forms of karate put a lot of emphasis on physical strength. Other styles style like Aikido and Judo rely mostly on technique as the primary concern while speed and power play different roles depending on which specific schools you attend.

Of course many of the most popular martial arts and kung fu movies are so impressive due to the incredible speed at which stars like Bruce Lee, Jackie Chan and Jet Li and fight and move. Visiting most Tae Kwon Do schools will also present you with various twig insect looking instructors who seem to be starving themselves in order to be lighter and faster, while classes are definitely centered on agility and speed not strength. However in the real world, being fast without having any power is not effective. If you hit your opponent a million times but do not hurt them or stop them it is futile. However, being fast is never a bad thing. Being in shape both in terms of being flexible and having low body fat can help you perform far better in class, but will also mean being better on the street. When it comes to reactions and striking combos, practice and time in class is the only way to really improve and maintain great speed.

Power and strength definitely have their role, not only in the street, but certainly in the UFC octagon and in your martial arts training as well. Bruce Lee even began weight training to improve his power and physique towards the end of his career. Certainly power means the ability to finish the fight quickly and stop your opponent or be able to fend off others if facing multiple attackers.
Would you rather just be fast and be able to hit an opponent 100 times in a row, but neither stopping or really hurting them, or would you rather be able to knock anyone out with one punch, BOOM, lights out? Obviously most would choose the latter. The only problem is when you can’t get in a great knockout blow and you have to hang in there till you can. Clearly the best solution is somewhere in the middle, train to be as fast as you can but also spend time in the gym or lifting weight at home in order to build up impressive striking power, no matter what your instructor says.