“Why would I ever choose adhesive over a static cling parking permit?”
Security is the primary reason to choose adhesive over static cling. Adhesive permits are a form of tamper-evident seals, which have been around since at least the Roman-era.
For example, static cling permits are easy to remove and give-away. To keep your permit in the right hands, adhesives are tough to remove. They will also generally tear if someone tries to remove the permit as well.
While static cling permits are for the inside of a car, generally on the windshield, an adhesive permit can be on the inside or outside. Not only does visibility complement security, visibility often helps out with routine permit checks: a bumper with no permit is easy to spot.
Whats right for you?
Ultimately it comes down to what is right for your situation. Adhesive is not really better than a static cling parking permit or visa-versa, they just have different applications and that knowledge can help you decide which one is right for you.