Let's take the example of gas vs. electric clothes drying.
1) Cost: In general, on average, gas is about 50% (not 67%) cheaper to dry clothes with than electric. And bear in mind that ALL of the thermal energy in a gas dryer goes to use. Not so with a gas rangetop. In one of those, only about 30% of the gas energy goes into the cookware. The rest is lost. Electric fares quite a bit better, with some 60% or more going into the cookware. So... do the math... it costs just about the same to cook with gas as it does with electricity.
2) If burning gas created brown stains, we'd see brown stained clothes coming out of gas dryers, and big brown stains on the walls of homes where the dryer exhuast vent exits. Neither are observed, so I must repeat that a gas oven is not more likely to cause grease, smoke, and grime on a kitchen's walls than an electric stove.
What MAY be at work here is that by nature, a gas oven must have more venting than an electric one. After all, the flames need not only oxygen, but a way to exhaust the products of combustion. So... there is likely to be more airflow through a gas oven than an electric one. This MIGHT account for more food vapors being released from a gas oven than an electric one. In any case, the solution is simple... turn on the darn range hood exhaust fan!
Also, in older setups, a gas oven was connected to an exhaust flue by design. Somewhere along the way, code writers apparently felt that such exhaust systems were not necessary. Modern gas stoves seem to have omitted this feature... too bad, it was a good one and should be reintroduced (in my humble opinion). It probably sent most cooking odors/vapors up the chimney instead of out into the kitchen. I'm guessing that a lot of electric ovens would benefit from a similar arrangement. A concern might be the loss of heated or cooled home air to the outdoors via the continually open range chimney. This is similar to the heat loss that may occur with in-room vented gas wall or space heaters. However by keeping the exhaust opening relatively low on the appliance (about a couple of feet or less off the floor, as is standard on older ranges), the loss of heated air may be minimized.
I have two electric ovens in my home (one is an older GE wall oven in the kitchen. The other is a in a vintage Frigidaire 30" drop in electric range in an enclosed patio. However, I never broil or bake meats in either one. Instead, I have a gas BBQ/rotisserie on an outer covered patio that gets that work. This keeps the greasy cooking odors out of the home and also allows for a much easier cleanup. I still use the electric wall oven for baking pizzas, cookies, breads, etc.
3) The odorant added to natural gas is a mercaptan (sulfur-bearing organic compound) that is present in extremely tiny amounts. It is consumed in the combustion process and the amounts used are far too minuscule to cause any residual odor or staining. Far greater amounts of sulfur-bearing compounds can be found in most meats, anyway (that off-odor that comes from burning hair results from hair's relatively high sulfur content).