Hello!
Where is the Speed / Size difference between AVI and MP4?
It might be the same.
AVI or MP4 is just the container (you can say a plastic can or a metal can) nothing to do with what is inside.
But I think you are getting things confused. You can estimate the size of a Re-encoding of a given file, that's what any Edition software does. Linears and NLE. But the record is already done, and with a small processing of it, the program will tell you an accurate estimate of the size of the encoding (re-encoding actually, as you are feeding it with a video already encoded).
Bandicam is a file creator. There is nothing before you press the record button. And what you will have depends greatly in multiple factors that can make the size to vary greatly for the same resolution and quality.
Think this way, if you plan a trip from A to B in a car, you can estimate the fuel it will take. But your Bandicam car only knows where is the starting point, then you go to some place where you are given instructions to the next point, and so on... How much fuel will you need?