Vapor pressure is a property of a liquid, and depends on two things: temperature, and the presence of solutes or other liquids that interact significantly with the liquid. Temperature is the assumed to be the same in both cases, so we compare the vapor pressure of water with the vapor pressure of Coke, which is water plus a bunch of non-volatile solutes and some dissolved CO2.
For a solution with one liquid and non-volatile solutes, Raoult's law states that the vapor pressure of an impure solution is always lower than that of a pure solution. So a non-carbonated drink has lower vapor pressure than pure water.
For carbonated drinks, the CO2 equilibrates inside the bottle according to Henry's Law, dissolving in the water at a concentration dependent on the partial pressure of the CO2 in the bottle. Since it's inert and equilibrated, it also behaves like a non-volatile solute, which further lowers the vapor pressure of the drink. So it turns out that the vapor pressure of Coke is actually lower than both pure water and non-carbonated drinks!
The reason for the counterintuitive answer is that the pressure inside a Coke bottle is mostly the partial pressure of CO2, not the vapor pressure of water.