The rule of thumb I've seen is that electric cars are about 25-75% better than fossil fuelled ones over their lifetimes, depending on energy mix and taking into account battery construction.
So it's hardly nothing - it puts them roughly in the same league as steam trains per passenger-mile.
This may depend strongly on how your electricity is generated. Probably best to assume the electricity is solar generated since, over the life of a new EV, that's likely to be the closest to the mark.
Last time I checked France was the best place since they accidentally have a very climate friendly power grid. Then you're left with just the embedded emissions from battery construction and the rest of the car.
Edit: this is wrong
Another fun fact is that short haul flights have fewer emissions per mile than electric vehicles for many current energy mixes.
Edit: wrongness ends (I hope)
It's hard to beat mass transportation no matter what you stick in the engine - it's just physics that power requirements scale mostly with cross sectional area, so it's more efficient to increase length and volume.
Edit: I'd remembered a per km figure and a per mile figure and forgot that the units were different. In reality, fossil fuel cars are about 35% better than short haul flights, so electric cars emit about 1/3 as much as short haul flights.
I don't have any hard data but I assume most car trips only have one necessary passenger.
("Necessary" being aimed at people doing the school run, where the parents wouldn't need to be there if the children got collective transport instead).
So it's hardly nothing - it puts them roughly in the same league as steam trains per passenger-mile.