Ironically, I just bought myself a cheap knock-off ACOG for my TAR-21. I'm curious of how that's going to help my groupings compared to iron sights.

A lot of factors can go into why your accuracy was off. Since the ammunition is corrosive in both guns, if you haven't been cleaning them almost immediately after you're done at the range, you can start getting some bad rust which doesn't help performance. With the Moisins, some of them have off sights without the bayonet on them I've heard. If you're using cheap surplus ammunition, that can almost make a huuuuge difference. It could also be you were having an off day, AKs aren't exactly precision weapons and holding a Moisin steady for long periods of time is a bit taxing.