Only those who do not actually spend much time cooking outdoors would say that a gas grill does not provide as much flavor as a charcoal grill. The truth is that the bulk of the flavor in grilled meat comes more from the skill of the chef than from the choice of fuel.
Neither a gas or charcoal grill does much in the way of smoking the meat, fish, and vegetables that are cooked. A wood or charcoal smoker will give the cooked food enough time in the smoke to permeate the food with the smoked flavor. Grills cook by heat and not by smoke. So, the flavor comes from the cook not the cooker.
Food cooked on a propane or natural gas grill will get that taste and feel of grilled food.
Even cooking a simple item like a hamburger will demonstrate how this works. The hamburger is placed raw on a metal grill over a gas or charcoal fire. The heat will build up in the metal of the grill faster than the areas where the meat is exposed to the flames. After a few minutes, when the hamburger is flipped, the familiar charred lines will be evident on the hamburger. These charred areas are the beginning of what produces that great grilled flavor.
Burning grease from cooking meat will generate additional flame, heat, and taste.
As meat cooks over any type of flame, the fats stored in the meat will begin to melt and run down onto the flames beneath. On a charcoal grill, this fat will hit the charcoal and begin to flame. On most gas grills, the flame is concealed beneath a shield. As the fat hits this extremely hot metal, it does not take long before the same type of flame as on a charcoal grill begins to blaze up.
Flame ups are controlled differently on gas grills than on charcoal grills.
In a charcoal grill, this flaming is controlled by water being dumped or sprayed onto it. This does not work as well on a gas grill. You often have to turn off the burners and shut the lid until the excess flame is extinguished. Both of these techniques will generate copious amounts of smoke and add that familiar smoky flavor to the meat in short order. Igniting the burner on a gas grill in good working order after one of these outbursts is no problem if the electric ignition is in good working order.
The grilled taste is reinforced if the sauce is allowed to caramelize over the heat.
While not everyone is a fan of sauces, most people who really like to grill outdoors enjoy the tangy taste of a good sauce. The sugar in the sauce will blacken and change flavors somewhat if it is allowed more time over the flame with the sauced side down. Re-applying sauce over the top of this caramelized sauce will give a greatly enhanced flavor. It is exactly the same whether over charcoal or gas.
Using a rub and tenderizer will enhance the natural flavor of the meat.
Not all meat will get tender over a grill. For lesser cuts of meat, using a good tenderizer is needed. Adding a rub of salt, pepper, and various other spices that you choose will give your grilled items a dramatic variation in taste. Once again, it is the seasonings and not the fuel that makes all of the difference. With a rub, you may choose not to char the meat as much so that the charred taste does not overwhelm the flavor of the rub.
Switching from a charcoal to a gas grill should only affect the flavor of the food until the cook learns to use the new grill.
Cooking techniques are what have to be changed when moving from a charcoal to gas grill or vice versa. Because the fires are controlled by different methods, how the food is prepared and cooked has to be modified a little. Also, learning to control the level of heat by a dial instead of using water or sealing off the flame requires a little time and effort.
If it bothers you not to smell charcoal or wood burning, add a metal box inside your gas grill and put some water-soaked wood chips inside. These will char and deliver any extra smoky smell that you are missing.