Firebird needs more power but is a better overall utility disc, whereas Gator is a better short range/approach disc. The Firebird will not go far for most people at all, likely it will fly midrange distances while the Gator will fly putter distances. But the Firebird will cut through wind because of its profile/speed, so it can handle high winds without losing as much distance as well as low ceiling power shots. It will also hit the ground faster because of this, so it is better for skip and trick/skip shots. Also because of the profile it is easier for most people to overhand, especially with power/distance in mind.
The Gator is slower so it is better at shorter ranges, when powering down a Firebird takes some experience so it doesn't fade immediately. Also the Gator will sit down better on approaches, where the Firebird can take huge skips. You just have to learn your angles and when to use them.
I feel like the Firebird is more versatile and will show you how to use this true OS utility disc. But if you want something more for OS approaches and short ranges, then look at the Gator. Also the Harp and Zone are good overstable approach discs, similar OS like the Gator but slower and shallower.