Both expressions can be used appropriately in a technical context. If they are really appropriate to the context, that is the question.
Of course you must use these expressions in a context where it is absolutely clear that you are aware that "consumption" is taken from engineering jargon and you know that energy cannot be really consumed, but only converted in other forms.
The same applies to power, since it is the rate of energy conversion ("consumption"), and the physical principle of conservation of energy applies always (at any time instant).
Assuming your audience is well aware that you know what you mean by saying "consumption", then sometimes it is equivalent to either say power or energy, because you just want to emphasize that some energy is "used-up" to do something, without particular interest on the difference between the two quantities (e.g. you might want to express that some machinery consumes lots of power/energy, without focusing on the details).
In some other context, you must be precise and specify energy or power according to what you want to express. For example, if you are computing the maximum power that a particular power line can deliver to a load, you can say that a load is particularly power-hungry by saying "it consumes a lots of power", or "it consumes 1000W (of power)"; talking about how much energy it consumes will sound strange in this case.