Bigger wing = More lift
The only way a smaller kite would outboost would be if it could be moved significantly faster creating significantly more apparent wind.
And only then
That's not how it works. There is a certain amount of kinetic energy available this is caused by the difference in speed between the rider and the wind. You can do whatever you want with that energy, if you loop the kite, you will extract all the energy at once and get a big downwind yank. Or you can use it to boost.
Now if you do not have a sufficiently large kite you can't extract all the energy. But if you do have a large enough kite, then you can convert all the energy to lift and lose some of it in drag. The way you can tell you have done this successfully is that at the top of the jump you will be moving at the wind speed downwind. At that point there is no more energy to extract from the wind, and you will have to use the potential energy (your height) in order to load up the lines. If your kite is too small you will feel a breeze even at the top of the jump because you haven't extracted all the energy.
If you use a kite which is larger than is large enough to extract all the kinetic energy all that happens is that the extra wind size will create drag and make your jump lower.
Most kiters like to kite inside a comfort zone. So they don't really experience this problem where the wing is not only large enough to extract all the kinetic energy but is also too large so that it creates drag and results in a lower jump.
Think about it like you are building a paper airplane.
You want to create a paper airplane that can land on your roof. One of the rules is that you can't launch like a baseball aiming straight up on the roof, you must aim it horizontally (this launch is like the horizontal kinetic energy we experience as kiters).
If you make the wings too small then the paper airplane will act like a baseball and just go curve downward like a projectile.
But if you make the wings incredibly large, no matter how hard you push the paper airplane, the big wings will eat up all of the energy and it will flutter down like a butterfly.
What you want is an arrowhead shape for the airplane a good shape to decrease drag, with the wings not too big, not too small. You also want to make some elevators on the back so it has the correct angle of attack. And now when you push the paper airplane straight forward, it will climb up and land on the roof.
This example shows the exact same forces we experience as kiters. Except instead of a hand pushing a paper airplane forward, instead we experience the kinetic energy as apparent wind.