The new Dragon ball series super has been getting a lot of credit lately because of the new arc (no spoilers). This story takes place after the Majin Buu arc in DBZ Kai. This season like its others tells of the adventures of Son Goku and his companions. Then as the series goes on Son unlocks some more of his hidden power, of the gods, to save the world once again from an enemy. So far it's had a lot of cool arcs like battle of gods, resurrection F, the Champa arc and the newest one coming out today!
But let's get down to it! Goku has great fighting ability and great training, while vegeta isn't only a genius but also is a very tactical and strategic fighter, which can sometimes leave him open for attacks due to overthinking. While Goku on the other hand is to relaxed and over confident at some points also leaving him wide open. They have fought before, they also fought in this arc and looked like the could be equals now, but are they actually stronger then one another ?
For all the fan of this series I don't really think I need to go over these characters in too much detail because it's quite popular. But Goku is an experienced fighter. Was trained by Grandpa Gohan by a very young age and kept on getting stronger later on beating king piccolo, to beating Frieza and reaching his first level of super saiyan. He then later on ascended his super sayian form in the android/cell ark and later after that he unlocked the super saiyan 3, the only form Vegeta has not obtained. Goku and Vegeta always had a rivalry and that is the main reason Goku befriends Vegeta. But I don't believe Goku would ever kill Vegeta because they had both stated that it is what strives each other to get stronger (their rivalry).
Vegeta on the other hand is almost completely different as "Kakarot", barely ever calling him by his real name Goku. Vegeta is smart, was born of royalty but his whole planet was destroyed by the space pirate Freiza, and Vegeta is the only saiyan left from his planet besides Goku. Vegeta going to planet earth to avenge his saiyan comrade Raditz. Vegeta gets his power from all his anger, rage and pride. Later on he achieved his super saiyan form after tremendous amounts of training to try to surpass Goku, he was later on able to ascend his form later in the cell arc, but never able to get super saiyan 3