Try a tank of each on your car and see how it does. It mostly depends on your driving...I'm a bit heavy-footed and so I'm sure I'm throwing away MPG on 87. The car feels a bit slower, so I push it a bit harder. If you drive conservatively all the time, there may not be a difference.
Turbo engines aren't a fan of low octane gas, so they pull timing and decrease power when they detect knock. This happens often on the Cruze - you can often feel little "pulses" in power between 2000-3000 RPM. Every time that happens, you're throwing away power/MPG.
87 octane does contain slightly *more* power per unit than higher octanes, BUT it has less knock resistance. For engines such as your Cavalier that do not benefit from higher octane by increasing timing advance, they will get the best MPG on 87 since they able to use the engine's full potential on that gas.
93 octane doesn't give you more power persay, but it lets higher-performance engines run closer to their maximum potential by not pre-igniting.