The argument is the same as whether it's more efficient to heat your house with a heat pump or heater. The theory says that a heat pump will win, and it does if certain conditions are met, but most people find that the heater wins in practice.
In theory, you can get more than 100% efficiency with a peltier device because it steals heat from the cold side and gives it to the hot side, but you can only steal so much heat from the cold side until the temperature difference is about 25 degrees where the peltier efficiency drops off, then you can't steel any more until you add heat to the cold side by external means, which would be great if it were in a waste heat exhaust from a machine or something or on a sunny day with a solar radiator added, but in that case you could use that added heat to supplement or replace the heater option to get more than 100% heating efficiency also.
In other words, there is a slight short-term gain while the peltier heats up, but the cost difference and complicated peltier arrangement would probably make the heater the logical choice. That's going to be the reason why we do our cooking and electric blankets with simple heaters.
Tell your mate to forget his peltier beer project and get a job selling heat-pump house heating if he's good at selling people stuff they don't need.