In general, I do not favor these, because they severely restrict what kind of vessels you can use on the stove top. Shape must be such that it presents a wide flat bottom, which pretty much eliminates woks. These vessels must also be of magnetic material, or a plate of iron has to be put beneath them to heat them, which can be less than satisfactory.

Of course, these things do exist, so manufacturers of cooking vessels do compensate for them where possible. Most multiply cookware has a highly corrosion resistant 300 series stainless liner, but on the outside of the aluminum or copper plate they use a 400 series stainless, which is less corrosion resistant, but is sufficiently magnetic to heat on an induction range.

I suspect induction tops provide better heat control than conventional electric elements, which have a lot of heat latency within themselves, but they just can't approach the convenience, universality and responsiveness of gas burners.