Randy Rhoads in my opinion was better, and he still to this day has a great effect on musicians, as well as the average person. Many of people are showing Randy Rhoads playing guitar, and listening to how Randy did things. They are reading his material as well as his biographies. While Eddie Van Halen is a good guitar player, he can not hold a candle to Randy Rhoads, who was an outstanding guitarist, teacher, and person. Eddie Van Halen faced his amps whiled doing solos so no one would steal his stuff while Randy Rhoads did what ever he could to teach everyone who wanted to know his stuff.
I would like to point out that my opponent made a mistake. Randy Rhoads did not die at the age of 16, but at the age of 25.
If you take a survey of people and ask if they know Rhoads most of them will not but Eddie on the other hand most people will know who he is. Randy also played songs other people (Zakk Wylde) can play but not the same if you know what I mean and only Eddie can play his solos and there is music out there that isn't perfect but makes it sound right.
Many people will know Eddie. To be honest, I knew of Eddie long before I knew of Randy. But, there are many guitarists better than both of them that aren't big names either. Randy Rhoads had his own unique style. Zakk Wylde tries to copy Randy's style, but admits that he can never nail it perfectly. Randy Rhoads is more influential as well. You will hear "that is very Randy Rhoadsish" more times than you will hear "that is very Van Halen Like". Please note that I am not trying to take anything away from Eddie Van Halen in this debate, as he is a very good guitarist that has an effect on my personal playing style. I just believe that fundamentally, Randy was way more unique. Of course, we will never know Randy Rhoads' full potential, because his life was cut off short at too young of an age.