The advantage of launching the rocket in the equatorial plane is that it will have more resultant velocity due to more radius of equatorial region.
The angular velocity of earth is, \[\omega=\frac{2π}{T}=\frac{2π}{24\;\text{hrs}}\] \[=\frac{2π}{24×60×60}=7.27×10^{-5}\;\text{rad/sec}\]
When a rocket simply takes off from the equatorial plane, the linear velocity of such a body will be $\omega R$ or $7.27×10^{-5}×6400000$ m/sec. But the rocket also has its launching velocity. So the launching velocity also gets added to it vectorially and the rocket achieves higher velocity.
But at other locations, the radius of the earth is less. So, the resultant velocity of the rocket will be less.