Gas models do have a flue going up through the middle of the tank which increases the standby losses. The other big advantage of a tankless heater is that you have, essentially, an endless supply of hot water. This will carry you through nicely when you have houseguests. On the other hand, if you have teenagers in the house, an endless amount of hot water available often translates into The Endless Shower. Savings from eliminating standby losses can disappear pretty quickly with someone taking 20 or 30 minute showers.
Most people think in terms of either electric or gas.
Natural gas is the lowest cost water heating fuel in most parts of the country, but don't get trapped into thinking that propane, or LP gas is similarly cheap. Your brother and neighbor may both be right. If your brother has natural gas, it's probably considerably less expensive than electricity for heating water. LP prices seem to fluctuate a lot, and in recent years have at times climbed above the price of electricity in some areas. The initial cost is high, but the operating cost is low.