Lots of speculation here. Anyone want to go looking for a well to wheels analysis? I think I did in the past and don't feel like looking now.
IIRC the gas powered turbines run around 50%, add in 10% loss for transmission lines, then maybe 10% charging and discharging losses (charge the battery, then discharge during usage). I come up with about 40% overall. Now add in nuke, solar, hydro and whatever might be feeding the grid, and... ? meanwhile it seems ICE is currently capped around 40%, diesel or gasoline, with the issue being that both hit 0% if just sitting and idling, and not a lot more when stone cold. Meanwhile that 40% for ICE is while under a decent load, anything other is not hitting 40%. Which is why hybrid can eek out more, even on the highway--it does the old pulse and glide, but without the attendant speed change.
IIRC prior discussions revealed that a dirty coal fired plant generated about the same CO2 per mile as a 40mpg gasoline powered car.
Hydrogen is just a fancy battery technology. Someone else can look into it, but I recall being told that compressing a gas is like 50% efficient--anytime you have heat being generated, you have heat loss.