D2's certainly can beat D1's. In your question, you specifically say both D1 and D2 are "very high". If that is the case when the player makes his decision, the two teams have roughly equal odds (no different that two D2 teams both being "very high").
All that being said, the D1 team has to put in significantly less resources to generate interest (especially when we aren't talking about a D1 D+ vs. D2 A+ or thereabouts), AND the D1 team likely has more resources AND the D1 team has all of first recruiting cycle to sign the player when the D2 team cant. I moved away from my D2 team recently but my policy there was never to battle a human D1. There are occasionally reasons where it can work out, like if its a very low prestige D1 school, the D2 team has better preferences or you think the D1 team has used up all of it's resources. The recruit also needs to have a late or RS2 signing pref too. But I would only do this very, very sparingly or you will burn your resources fast.
I did regularly battle SIMAI D1 teams. For these, you need to knock them down to very low by sending a CV and a few HVs and then the SIMAI team will stop try. Don't send the house though (20 HVs and a CV) because there is still a pretty decent likelihood a human D1 team swoops in late in RS1.