If two or more different electric heaters have the same power consumption are they providing the same amount of heat to the room? If I have a number of different electric heaters. Say one has coils which heat up, one is a fan heater and another is an oil heater in which the oil is heated by electric coils internally (They are all electrically powered and plugged into the mains). 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?
Of course when you turn on the heaters initially the appliances themselves must warm up, but once they have all reached a stable temperature are they providing the same amount of heat?
The law of conservation of energy implies "Yes".
Unless I am overlooking something.  
 A: 
and assuming that they all genuinely use 2000W of power

This is the crucial assumption. If both have real power 2000 W, this means 2000 W of heat introduced into the wires and then (by assumption of stationarity of temperature of the heater) this heat leaves the wires and goes into the heater environment.
But equal heat introduced per unit time does not mean equal effect on average temperature or equal efficiency of operation. Bigger heater with greater exchange surface will operate on lower temperatures and will heat up the air more evenly quicker (because of energy losses from the room). This can be more efficient if we want to achieve same temperature everywhere as fast as possible, or less efficient, if we want to heat up only our frozen legs.
Also in practice, even if two heaters have 2000 W written on them, this does not mean that actual consumption is 2000 W all the time. For example, as the heat producing wires get hotter, their ohmic resistance increases, so the effective value of current should decrease and real power should decrease as well. The only way to be sure of the consumption of the heater is to measure it with a wattmeter.
A: Some heaters are more biased to the infrared (red glowing coils) and these can send more heat to the walls of the room instead of directly to the air, this may be undesirable.  Also a heat pump is an example where 2000 watts of energy can produce more than 2000 watts of heat, heat pumps require access outside the room to a heat source (like pipes in the ground).
A: 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).
