As mentioned above, in D2/D3 prestige doesn't have much of an impact in battles. It's really all about money. So in your hypothetical situation, if a higher prestige school invests a couple scouting trips and a HV, you could win the battle with a couple scouting trips and 2 HVs.
Just an aside, scouting trips are a very inefficient recruiting tool. You should only use them to gather information about "high-highs" or pull a player down. If you are recruiting a same division player, use only HVs or CVs (depending on the distance from your school), and optionally guaranteed starts/minutes.