Advantages
Safe to the touch - good for those with small kids
Very energy efficient compared to other electric cooktops
Heats instantly - very little warm-up time
Looks stylish
Flat surface is easy to clean - food doesn't 'bake' on
Disadvantages
Can be expensive
Requires ferromagnetic (i.e. stainless steel or iron) cookware
May be complicated to repair or replace
Electric coil or hotplate cooktops:
Advantages
Cheap to buy and repair
Works with any type of cookware
Good for low-temperature cooking and simmering
Disadvantages
Slow to heat up
Slow to change temperatures in general
Relatively inefficient
Electric ceramic radiant cooktops:
Advantages
Looks fantastic
Flat surface is easy to clean
Reasonably responsive to changes in temperature
Works with any type of cookware
Disadvantages
More expensive than conventional coil or hotplate cooktops
May be complicated to repair
More effort to clean than flat surfaces
Gas burner cooktops:
Advantages
Instant heat
Very responsive to changes in temperature
Cheap to operate
Can accommodate wok burners and special trivets
Can char-grill capsicums on the open flames like they do on TV.
Disadvantages
Requires a supply of gas
Harder to clean than flat induction or radiant cooktops (enamel is easier to clean than steel or glass)
Greater risk of fire or combustion due to open flame