There are 2 scenarios to this situation. Take them both into consideration because I have experienced both of them.
Most of the time, Groudy is faster. Here is the situation in which he could indeed win. Groudy uses EQ. If Kyo stupidly uses Water Spout, there ain't much damage there. EQ does enough damage to kill Kyo in 2 hits. Also, Surf would not kill Groudy one hit. Maybe with Drizzle, but he still could easily live.
Now for the scenario Kyo would win. Groudy goes EQ again. This Kyo gets smart an' uses Hydro Pump an' hits. Easier in NB. The Kyo could also pull Quick Claw an' hit with Surf perhaps twice, if he gets lucky.
These scenes work with either Drought or Drizzle. Drizzle just helps Kyo a bit more durin' the last scenario. This is of course 1 on 1. If there were teams, each side would have the opportunity to power up before attacking.
Baby I like it.