Difference between small/medium/large player databases when creating new save?

I'm exploring a new save (I tend to like Journeyman style) and narrowing down my league list.

What is the actual difference between selecting X size player databases besides the game speed?

It's not clear to me how this affects the actual game. For example, I can select the same leagues, but dial up and down the amount of players that are populated on a the actual database?