I control 8 runes and 4 units. Opponent controls 4 gears and 8 runes. After Divine Judgment reasolves, what will remain on the board?

It depends on the choices, but here's what's guaranteed: after Divine Judgment resolves you'll have at least 2 of your units and 2 runes, and your opponent will have at least 2 gears and 2 runes.

Resolution works in turn order — you choose first (2 units, 2 gear, 2 runes, 2 hand cards), then your opponent chooses the same categories (FAQ #994). Every card not chosen is recycled simultaneously.

Key wrinkle for your board: choices aren't restricted to your own cards (FAQ #5977). You have 0 gears, so you must pick 2 of your opponent's 4 gears to keep — those 2 survive no matter what. Your opponent has 0 units, so they must pick 2 of your 4 units to keep — those 2 survive no matter what. Each of you keeps 2 of your own runes (2 each remain).

What survives beyond that is up to the second chooser. If your opponent picks the same 2 units you kept, your other 2 units get recycled (you end with 2 units). If they keep 2 different gears than the ones you saved, all 4 of their gears survive. So the realistic end state: you: 2 units + 2 runes; opponent: 4 gears + 2 runes — with the caveat that cooperative/overlapping picks can leave more units or fewer gears.