Hydronic electric baseboards are not any more thermodynamically efficient than convection electric baseboards. One watt of electricity fed through a resistive heating element produces one watt (3.412 BTU) of heat. It doesn’t matter if you use a simple resistor, fill the cavity with oil, or stack rocks on top, it’s the same amount of heat.
The difference, as Jean-Paul points out is the comfort level in the room. Simple resistive heaters heat a space quickly, which is great if the room is cold to begin with, but once it reaches desired temperature they must cycle on and off to maintain it, which may not be desirable depending on how close you are sitting to the heater.
Oil-filled units take advantage of a feature called, “thermal inertia.” It takes longer to transfer the electric heat into the room, slowing down the temperature rise, but once the unit cycles off, the oil continues adding smaller amounts of heat so the room cools slower as well. Some people find this more comfortable.
Makers of oil filled electric heaters try to bill this change of how the heat feels as an incentive to set your thermostat lower, and frame it as an efficiency increase, it isn’t, and at the end of the day, if it’s 40 degrees outside and your room is set at 70, the exact same amount of BTU’s, and watts per hour will be needed to keep this temperature differential. So an oil filled 1500 watt heater produces 5118 BTU’s, exactly the same as the simple 1500 watt electric strip. The efficiency is the same.
Power line losses
There are indeed losses in power line transmission as you suggested, but these are not evident in your electric usage since the meter is on the side of your house, downstream of all the transmission lines. Transmission and distribution losses in the United States are estimated at 5%. While your heater might be using 1500 watts, and your electric meter is accurately tracking it as such, the power plant might have to produce 1580 watts to make it run, with the remaining 80 watts heating lines between you and the power plant.
Natural gas heating costs
Natural gas and other fossil based fuel heating systems have losses too, but the end cost of these fuels “per BTU” is generally far less than electricity, this lower cost usually more than offsets the heating system losses in the home. As always, your mileage may vary.