Ice cubes in a drink

[T50_Omaha8]

Some friends and I became involved in an argument at the bar tonight. Please help me settle it.

There are two glasses sitting on the table. Both glasses contain only liquor and ice, and at the time of the argument the top of the liquid is at the same level for each drink. One drink is 'fresh' and is full of ice all the way down to the bottom of the glass, while the other drink has been sitting for a few minutes so there is only a small amount of ice remaining. Neglect any ice floating slightly above the surface of the liquid.

After a discussion about which drink contains more liquor, one party proposes a bet: if we were to wait several hours until all the ice in both drinks melted, the older one that is partially melted would have a higher liquid level.

The others argued that the fresh drink that was full of ice would have a higher liquid level after all the ice melted.

This bet could not have been carried out for obvious reasons, but if you have to back one of the two stances, which would you back?