The Case for Gas
Instant heat, immediate temperature change. No need to wait for metal coils to heat up or cool down. No need to worry about that delicate sauce getting overbrowned. Gas is also more cost effective. Or is it? Certainly not if your source is propane. If you have natural gas stubbed into your house, then the cost of cooking might be as much as half that of using an old electric stove to prepare the same dish--that is, assuming you have a modern, efficient, pilotless gas stove. In real terms though, the difference in cost over a year's time is not significantly different from that of using a similarly efficient electric stove. Cooking with gas does allow for more precise heat adjustments. It is much easier to control the exact amount of heat generated beneath the cookpot. It's perfect for those epicurean cooks out there.
The Case for Electric
"I don't like that the gas burner discolors the bottom of my good pans, never mind that there's that perpetual flame and the worry that gas will escape and create an explosion." For those who voice such concerns the electric cooktop, in one of its many manifestations, will be the appliance of choice. Though cooking performance may lag slightly in comparison to its gas equivalent, most cooks would rarely be inconvenienced unless, of course, there's a power outage. Very few cooking techniques using the gas stove cannot be duplicated, and sometimes bettered, by an electric stove. Popular choices in electric cooktops include traditional coil, halogen, or magnetic induction. Cleanup and overall safety may also favor the electrics, but only marginally.
Cookware Makes a Difference
Whatever small advantage one type may have over the other could easily be mitigated by the selection of cookware. Often, taking advantage of a stove's strength requires the use of a particular type of cookware. For example, tinned-copper (expensive) responds instantly to changes in heat output. That's great if you're using a gas stove. Cast iron, on the other hand, will hold its heat for a long time, even if the heat is turned off entirely. For most of us with an eclectic collection of non-stick, anodized aluminum, glass, stainless steel, enameled porcelain and copper, the choice of flame or coil makes little difference in the final dish.
Both electric cooktops and gas cooktops are available in a wide variety of configurations and options. In general, the electric version offers a slight price advantage given equivalency of features. This is particularly so when installation costs are factored in, since the cost of configuring a 220 line is considerably less expensive than installing gas lines.
OK, So Which Will It Be?
Having used both extensively, I'll cast my lot with gas. I like seeing the flame and being able to adjust it visually. I also like using copper cookware and feel, right or wrong, that the combination of gas and copper gives me the greatest degree of control over the cooking process. If I need to buy a carbon dioxide monitor to prevent a gas buildup that might immolate my neighborhood, that's an expense I'll gladly sacrifice.