Gas hobs waste a lot of heat that goes up and around the pan.
Electric induction hobs waste very little heat as the base of the pan is the heating "element" in direct contact with the food / water in the pan.
Very true and this is the major problem with gas, both oven and hob need ventilation, so they put moisture in the room and heat in the room, the cooker hood can remove some combustion products and some of the heat, but kitchens with gas appliances can be really hot in summer, and in winter the use of the cooker hood can also mean cold drafts.
Since gas around ½ or less the cost of electric there is little direct saving using electric, however with the old electric ring the electric hob was slower, but that is no longer the case, with the induction hob electric is far faster.
The other is control, an induction hob can be used direct to melt chocolate, no double pan with water, can be used direct, it can both turn down lower and turn up higher than gas, plus loads of safety features, auto turns off when pan removed, auto times out if left on, child locks, however my grand children seem to think it is funny to put on child lock as wife can't work out how to remove it.
The oven on mine has 12 options, with or without fan, side heat, top heat, back heat, and mine does not have steam, it has returned to what was normal with a solid fuel oven where setting the dampers would change what was heated, the problem is Mrs Beeton's cook book was re-written for gas, and the damper settings for use of oven removed, so one has an all singing dancing oven, but only the manufacturers instructions on how to use it. So it involves some learning, we found closed door grilling was great, the fan means under the food is still cooking, so where with normal grill continually moving the food, with closed door turn food once.
Clearly gas ovens produce water as the gas burns so the food is more moist, but you can get steam option, and no way to get around the fact using a wok you really need gas, as a electric wok is too heavy.
We found a problem with pans, we thought a stainless steel pressure cooker would work, but no, does not matter if steel or copper, the base must be magnetic, the replacement pressure cooker did work, but we found the pressure had changed, old one 15 PSI and new one 6 PSI we did not even realise there were different pressures.
Biggest fault with mothers was touch controls, ours has knobs so great, but like gas you don't need to lift a pan with an induction hob, control is instant turn it off and heating stops, but if you need to repeatedly touch some touch control then all you have gained is lost, the touch control with halogen hobs was good as wipe clean, but the induction surface does not get red hot like the halogen, so food does not bake on if spilt, so no longer a need for touch controls.
We got the induction for mother for safety, the hob is heating by pan, not other way around, so if you touch the hob it is not that hot, so any burn is not as serious, however she was in a wheel chair, so viewing the touch controls from a lower angle, and we realised she could not see where the controls were. We had to remove the induction due to her having a very old pace maker which may have been affected with an induction hob, 4 weeks latter she had a new pace maker fitted and we could have kept the induction hob.
Our hob slightly lower than work top, so any spill is retained on the hob, hers was about 1/8" proud of work top, so any spill ran off the hob onto work top, getting anything left on work top wet, since the induction does not get that hot liquid does not turn to steam and stuff in liquid bake onto hob, so it will run onto work tops if the work top is lower.
Some touch controls do have a single off button for each hob, but mothers you selected which heat area, then pressed up to 10 times to completely turn off hob, so not all touch controls bad, but learn from our error. When looking at demo models bend down to child height and see if a child would see the warning hob hot light.