Choosing a hob pits efficiency against the price of the fuel. Induction is the most efficient way to cook on a surface, putting almost all its energy into the pan, but electricity costs more per unit than gas, so the cheapest hob to run is not as clear-cut as the efficiency figures alone suggest.
Why induction is so efficient
An induction hob heats the pan directly through a magnetic field, so very little energy is lost to the surroundings; the hob itself stays relatively cool and the heat goes where you want it. A gas flame, by contrast, licks around the sides of the pan and loses a good deal of its heat to the air, and a conventional electric ring wastes energy warming the element and the ceramic. In pure efficiency, induction is the clear winner, gas the laggard.
The price-per-unit twist
Efficiency is only half the sum. Because each unit of electricity costs considerably more than each unit of gas, induction's efficiency advantage is partly cancelled by the dearer fuel. The result is that, on running cost alone, induction and gas often end up broadly comparable, with the balance shifting as the relative prices of gas and electricity move. Neither is dramatically cheaper to cook on than the other for most households.
The other things in the balance
Cost is rarely the only factor. Induction is faster to heat, responsive, easy to clean with its flat surface, and safer with no flame and a cool top. Gas gives the visible flame many cooks prefer and works in a power cut. If you are moving away from gas in the home anyway, perhaps towards a heat pump, an induction hob fits that direction. These practical differences often decide the choice more than the running cost does.
Whatever you cook on
Good habits cut hob energy on any fuel: use a pan that matches the ring or zone size so heat is not wasted around the edges, keep lids on to bring things to the boil faster and hold them there, and turn the heat down once a pan is simmering rather than leaving it on full. Those small disciplines save more, day to day, than the choice between fuels.