Two huge advantages:

1. accelerated depreciation (write down a percentage of the asset's value per year) which reduces your taxable income. Accelerated depreciation means that you can now write down more in the beginning than normal - not sure about the percentage.

2. interest expense off of any mortgage used to buy your share - you can reduce taxable income by the interest expense paid during the year.

Fractional ownership allows you to treat your share as an asset (and, as a result, you can write off depreciation expense annually). That is a big benefit that you don't see when you charter airplanes unless the charter expense is a business expense (then you can write that off too). Charter flights for personal reasons/travel cannot be expensed.