Well the phrase "leeches calcium" comes to mind when I think of the carbonation thing but I can't find any sources on it... (maybe that means something? 
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As Steve already mentioned, there is no such effect (aside from a minimal effect on teeth similar to drinking orange juice... remember to brush, kids).
What the phrase "leeches calcium" should say to you is a clearly over-emotionalized non-scientific term that might be used in some urban legend about the dangers of bubble gum, government conspiracies with microchips implanted in your teeth and money, and KFC making mutant chickens that package themselves into happy meals
Those sort of weird claims are usually made popular by websites that don't check their facts, and their claims are usually not about carbonation itself but about other perfectly fine things that also definitely don't "leech calcium", like phosphorus or phosphoric acid (which we know doesn't really affect calcium as it's been conclusively tested).
About the original question, that's like asking what is better between water and water with some color in it, or maybe even between water in a blue bottle or water in a red bottle.
The answer should be obvious, and the real question should be why would anybody think that adding bubbles or color or using different container shapes might make it better for you, rather than being a mostly harmless but unnecessary addition.
There is a -purely statistical- association between carbonated drinks (especially sugary sodas) and less intake of milk and proteins, which then can result in some slight decrease in bone mineralization in some groups (teenager girls from Northern Ireland, for example, but not boys from the same area). But again it's more of a correlation and not quite a cause and effect, chances are if you don't have a good diet you are less likely to drink milk and eat eggs or something and more likely to just drink sodas and doritos chips instead.
