Does more damage? Dunno really, I don't use any add ons on pc, so when I see my abilities hit for far more damage than usual, then I know it was a crit.
In PvP, I roughly know how much my Surprise attack will chunk a HP bar on someone with 20-25k HP and around 15k Armor.
If my SA chunks a bigger portion than usual, I figure I've crit or maybe they have low HP and armor..
Yeah, this is what's it's like on console right now and why we've been demanding a massive UI update.
I don't use addons, even on the PC. I don't think there is a way to tell, other than the amount of damage it causes looking at their health bar.
Fortunately a combat log is coming to the console version soon, so hopefully that will tell you.
The consoles don't show damage numbers for each hit, so it makes things quite subjective.
Critical Hits which kill enemies with elemental damage have an additional death animation: Burning to ash for Fire, Freezing solid and then turning to a pile of snow for Cold, or similar.
PS4 - NA - AD
v16 Khajiit NB Tank
40 Breton Templar Healer/Tank