With regard to efficiency, I was considering only the efficiency of converting electrical energy to heat energy, not the efficiency of how that heat is used to cook food. For electrical efficiency it makes no difference whether you use a nichrome heating element or a halogen lamp. Both convert electrical energy to heat energy with the same efficiency. A halogen lamp may have an edge in speed of response. The halogen gets hot almost instantly and immediately radiates a lot of infrared energy. The nichrome heating element also gets hot quickly but is usually accompanied by a significant thermal delay.
In an electric-powered convection oven, air is heated using the electrical element by conduction of heat from another surface because, as I mentioned in another post, air is relatively transparent to infrared energy and does not absorb much heat from infrared radiation. In a nichrome-heated convection oven the circulating air passes over the incandescent nichrome element and absorbs heat energy by conduction therefrom, transferring that heat to the food by forced-convection of the heated air, which then transfers the hot-air heat to the food by conduction. A similar process occurs with halogen heated convection ovens, except the halogen lamp radiation is usually directed at the walls of the cooking vessel, which absorbs the infrared radiation, gets hot, and the heat is then transferred by an air-circulating fan to the oven contents. For a given power input, both methods are equally efficient in converting electrical energy to heat energy.
The overall efficiency of either type of convection oven, and how long each model takes to prepare food, depends on many factors. The consumer has no control over most of these factors except in their choice of which model to purchase. Marketing folks are aware of the limited amount of information available to the consumer, and they feel free to use this information vacuum to their advantage, touting all sorts of claims that are difficult to verify.
I think the most important factor affecting oven efficiency is how well it is insulated to prevent heat loss. AFAIK, none of the table-top convection ovens is particularly good in this regard. In my home we use three fairly efficient methods of cooking: a gas-fired convection oven that is well-insulated; a table-top "crock pot" heated electrically; and a 1200 watt microwave oven with a motor-driven turntable. You can't get more efficient than a gas-fired oven, unless you heat with sunlight. A huge amount of energy is sacrificed to convert low-quality heat energy into high-quality electrical energy for wide area distribution. It doesn't matter whether the heat source is gas, coal, oil, or nuclear: a lot of the heat-energy in the fuel is "thrown away" in the process of generating electricity. OTOH, almost all the heat-energy in natural gas is captured by combustion in an oven, although some escapes from the exhaust vent. I prefer natural gas heat for cooking as well as home heating, but the "crock pot" is surely convenient: load it up in the morning, eat dinner from it in the evening... all for a few cents worth of electricity. As for the microwave... it's pretty good for heating up a cup of coffee, or a bag of frozen veggies, or even making a cup of tea (if you aren't a stickler for tea-making protocol) but we don't often try to cook a whole meal in the microwave. However, of all the ways to electrically heat food for cooking, the microwave wins hands down for speed and efficiency of electrical energy use... in my opinion of course. Your mileage/kilometers may differ.