It's not quite as simple as a fuel burn on a new engine alone - The fuel burn to generate the required thrust increases slightly as the engine ages and they all do this at slightly different rates. So, while one engine may well use a little less fuel when new, its advantage may disappear after a couple of years. There's also the installed weight consideration; a threee-spool engine will always weigh more than a two-spool, but can sometimes burn less so you have to look at payload (you can lose four tonnes or so pretty quickly) versus how much fuel you need to fly long sectors, etc.
There's many other factors, but I hope you get the idea.