I depends on you location and driving in the city e.g. Prius can have less total CO2 emission than Tesla S if the electricity comes from fossil fuels.
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I find that hard to believe. So you're saying that Prius, despite being more complicated (as it needs to route both internal combustion and electric power to the wheels), has an electric motor/transmission more efficient than Tesla and internal combustion engine more efficient than power plants? The only way I think that's possible is if weight is taken into account, Prius seems to be a bit smaller and thus possibly lighter than Model S...
I think this is possible if the Tesla’s electricity is coming from burning coal, which produces ~double the CO2 emissions per unit energy compared with gas. (Though this seems annoying to actually calculate, so I haven’t.)
You would not be looking at efficiency from a energy/$ perspective, which is what industry power generators care about, but rather energy/ton of CO2, which they rarely care about.
Are you taking into consideration the loss of energy in power transmission and distribution?
(I also find the argument hard to believe, but I'd be interested in seeing a proper comparison)
Well, yeah, that's basically equivalent to saying that you'd save money by running an internal combustion engine at home, rather than buying electricity from the grid. Sounds unlikely - although there are potential savings to be had if you take into account the heat generated, which is lost from the powerplant but a household could use it for heating - check out mCHP https://en.wikipedia.org/wiki/Micro_combined_heat_and_power
It's more like saying that you'd save fuel by running an equivalent ICE at home. You'd be unlikely to save money, because of economies of scale.
But I imagine that fuel is the vast majority of the cost, at least operational cost... and the initial investment is also at least to some extent dependent on the resources used (energy, matter).