Induction hobs are BRILLIANT. I bought a single induction burner when they were really quite new and was converted instantly. I gave it to someone a few years ago, and bought myself a newer one.
Actual disadvantages :
1. If you do a great deal of cooking in a wok you won't like it anything like as much as a powerful gas burner, and if you often want to char the skin on peppers over an open flame, it's obviously no good for that.
2. If you rely on hob cooking to help keep your kitchen warm in winter, you might have to settle for a cooler kitchen, as there is far less heat wasted than with any form of conventional hob. However, to counter this, your kitchen will stay cooler in summer, so its swings and roundabouts.
3. You might need to buy new pans.
Precautions:
IMPORTANT If you have a pacemaker, or any other sort of implanted electronic device, check with your doctors before using an induction burner as to whether or not it will be affected by electromagnetic forces at such close quarters.
Other than that one caution above, they are safer than gas or conventional electric for everyone in every way, and the air quality in your kitchen will instantly improve if you've previously used gas. I always said - being a long-ti e gas hob user - that I could never use an electric hob with any degree of pleasure. An induction burner changed that, even my first one being comparable in responsiveness to a gas hob.
My induction burner - which has a specific 'boil water' setting - boils water faster than does my electric kettle.
If you're unsure about investing in a full hob, I suggest you buy yourself a single burner to try it out and get used to it. You can get a decent single one for not very much money and it will always come in handy for yourself or others. I discovered that most of my existing pans were ok for induction; I just needed to get a big stockpot and a small frying pan.
Be aware that they can make odd noises.