I am not an expert on the topic but i will try to answer in a laymans term.
Well first off all horse power is the amount of power produced by the car when fuel is burnt. There are many ways to increase the horse power. By increasing the amount of air flowing into the vehicle or by increasing the amount of fuel it is burning. Ok now lets us try to increase the horse power of our cars and lets see what effects it has.
Lets start cranking up horsepower of our car from 100 hp:
Now to increase the horsepower we may just get a better air flow system. Engine produce power by burning up fuel, the better they burn , more the power is generated. For fuel to burn better we need more oxygen, were do we get that, obviously increasing amount of air flowing in the engine(not too much though, we don't want a air heater).This blog explains various ways to do it. Using those methods you can increase up-to 50 horsepower. Now one thing here to notice that even you have now increased horsepower, it will also result in performance and a better fuel efficiency of the car.
So we increased our cars power from 100 to 150 and that also with much better performance and fuel efficiency.
Ok now lets try to increase it up-to 300
Now going on with better air flow will now not help us much so what we do.
Remember last point engine generate power by burning fuel. So now to increase the power we have to increase the amount of fuel going in the engine. More means bigger blast, means more power.
Ok so why does it gives less mileage than the 100 hp one. Well cars with 300 hp(those are too many horses there, look out while driving) are generally designed to go at a higher speed. Generally these cars give better mileage at higher speed as compared at a lower speed, cause the have more fuel running in the piston compared that to 100hp car most of the fuel is not utilized correctly.
It is same like driving your 100 hp car in 2end gear, well you are capping the full potential of you vehicle no matter how aerodynamic it is, it's going to consume more fuel
Hope it helps.