So really, you will NEVER do the same amount of damage you're doing to someone in pvp than in pve.
Someone correct me if im wrong, though.
Thats right (although I think the damage gets boosted first - doesnt really matter however). But if you hit someone without any PvP equipment (so, 40% resilience) with over 66,67% PvP power (which is impossible to obtain), you would still do the same damage. 100 * 1,6667 * 0,6 = ~100.
The differences may come from different armor values. Judgment should always hits more consistently than CS, and even harder with targets with ~40%+ armor. Considering my values, I hit for around 14k with Judgment (no buffs) and an average of 22k with CS + Mastery (no armor) on my PvP equipment. PvP power/resilience will affect both the same way, but CS got affected by armor, which can be as high as 50% for a holy paladin, or as low as 25% with a warlock (as far as I can tell). I dont know about PvE armor values, if they are constant or not though.
Judgement scales better with str increase - and get direct affected by Inquisition; it also has the glyph which raises its damage by an additional 20%. CS only got 4% increase by Judgment' debuff and got affected by Mastery (with itself got affected by Inquisition), other than AW and HA. So it really depends on the target armor and on how buffs you were under. So check that in both PvE and PvP scenarios to see why your Judgment is hitting for so low.