It's not about electrical power. Of course it does play role. It's actually about ERP and the radiation pattern which determines the strength of the signal in a particular direction.and can hence generate more electrical power.
It also depends on how T/R module is connected to the antenna through transmission line. Because there is a significant loss of power during transmission. So output power is not necessarily the final value. What power does antenna receive and how it generates the pattern that is very important.
There are thousand factors determining the signal strength.
It is very tough to determine without experimenting in different environments speed, power etc.