When people talk about efficiency with a dryer, they're usually talking about how much it costs to run the dryer. This will depend entirely upon the cost of electricity vs. the cost of natural gas in your community.
There is no such thing as an energy-efficient dryer, as a gas dryer will always use the same amount of gas to produce a given amount of heat, as will an electric dryer use the same amount of electricity to produce a given amount of heat.
The air circulation in a gas dryer vs. electric is exactly the same, as is the drying performance, because the only thing that is changing is the source of the heat, not the way that heat is distributed or how the fans and ventilation work.
The best dryers use a combination of air cirulation and moisture (rather than air temperature) sensing to ensure a dry load of laundry. If you're finding wet spots in your laundry, your dryer probably uses a thermistor to sense the temperature of the outgoing air to determine if the clothes are dry. These are not terribly reliable systems, and most dryers have moved to a moisture sensing system that uses two metal strips to detect water in clothes as they move through the drum.
Your dryer also might be too small for the amount of laundry you're attempting to dry. A safe approach is to have a dryer with a capacity of at least 7 cubic feet (certain exceptions do exist). The more room there is for clothes to move, the more room there is for heat to travel and the faster moisture is whisked out of the dryer.
As for gas odors, that has more to do with the soundness of gas connections than anything. A gas dryer does not affect the odor of clothing unless there is a poor connection somewhere in the gas line.
Repair rates are dependent upon many factors, and it's hard to quantify exactly which version has more repairs, and whether those repairs are based upon where the machines reside and how they're used or whether it's due to a fundamental virtue of the machines themselves.
The simplest rule: If you already have a gas hookup, stick with gas. If you already have a 220v outlet, go with electric. If you have both, get electric, because they cost less up front.