First, Eloquent automatically converts it’s timestamps (created_at, updated_at) into carbon objects. You could just use updated_at to get that nice feature, or specify edited_at in your model in the $dates property:
protected $dates = ['edited_at'];
Now back to your actual question. Carbon has a bunch of comparison functions:
eq()equalsne()not equalsgt()greater thangte()greater than or equalslt()less thanlte()less than or equals
Usage:
if($model->edited_at->gt($model->created_at)){
// edited at is newer than created at
}