Ice melts faster in water than in soda. This is because soda has sodium (salt) in it, and adding sodium makes ice melt more slowly than it will in plain water. In order for ice to melt, the chemical bonds that join water molecules must be broken, and breaking bonds always requires energy. Adding sodium to a solution means that it takes more energy to break bonds than it takes in plain water, which slows melting.
Water is a critical substance for life as we know it, and in part its unique properties can be attributed to the kind of chemical bond that forms between atoms in water molecules and between water molecules themselves. The oxygen and hydrogen atoms in water molecules are joined by hydrogen bonds, which are weak bonds that continually break and form as the molecules move about.
Water molecules have a lot of mobility due to the weak hydrogen bonds that join them. This is why water is liquid at temperatures above 32 degrees F (and below 212 degrees F, where it becomes steam). The warmer the temperature is, the faster the atoms in the molecules move. As the temperature drops to 32 degrees F, the atoms move more slowly until finally they "freeze" and crystallize as water turns to ice.
The melting point is the point at which ice changes phase from a solid to a liquid. The melting point of plain water is 32 degrees F, but the sodium in soda means that it must be significantly colder than 32 degrees F before the ice will melt in soda. This is because sodium lowers the melting point of ice, meaning the solution must be colder before the ice will melt.
The sodium in soda lowers the melting point and makes the ice melt more slowly than it would in plain water because with the addition of salt (or any substance), there are fewer free-water molecules available to form bonds together and "freeze" into ice as the temperature drops. Heat must be removed from the solution to break bonds and melt ice, which lowers the temperature of the entire solution and the melting point of ice in soda.
People living in cold climates may find the fact that salt lowers the melting point of ice counter-intuitive, as salted roads are the norm in snowy areas. But in snowy conditions, salt keeps roads free of ice. As discussed here, the addition of salt lowers the temperature at which water will freeze. Thus, in the presence of salt melting snow will stay liquid at low temperatures instead of turning to ice and making the roads slick.