Let us talk about a convection current. Having a heater with a big surface the convection from this surface to the colder surrounding will be bigger as from a heater with a smaller surface.
Does this mean that a heater with bigger surface will heat a room faster? For electric heaters that isn't the case. Indeed a heater with a smaller surface will heat the room more than a heater with a bigger surface. To understand this one has to remember that for electrical conduction materials Ohms law is nearly linear only for small changes in temperature. The electrical resistance grows with higher temperature. By this a heater with a smaller surface will heat a room more than a bigger heater.
But this is not the full truth. Making a heater device from semiconductive material - and this is really possible - he resistance changes to lower amount with higher temperature. So a bigger heater with semiconductor heating device will heat up the room better than heater of smaller surface.
Not sure that this are all influences :-).
Ok there is one more moment. If the power source (a power plant for example) is really big in relation to the power consumption device (the electrical heater) all above said is ok. If the power source is small (a car accumulator for example) in the moment the accumulator is exhausted both heaters had gave the same amount of heat to the room. But different heaters reached this moment at different time.
Someone else has an idea?
If these heaters all show specs of 2000W, and assuming that they all genuinely use 2000W of power then are they providing the same amount of heat to the room?
So the specs draws not the full picture. In reality the power consumption Inder temperature influence changes (a little bit).