Preventing Eye Ptosis from Botox?

How to avoid a droopy eyelid after Botox injections:

Go to a qualified experienced injector--incidence should be less than 1%
It turns out many people who end up with ptosis already have sub clinical ptosis. When the frontalis muscle is injected over aggressively to treat the horizontal forehead furrows, the ptosis can be unmasked. This is because the forehead muscle is compensating for the weakened eyelid muscle. Removing this compensatory muscle causes the eyelid to droop.
Injecting too close to the eyelid muscle when treating the glabella, or the 11 lines.

It has nothing to do with the product and everything to do with the person doing the injections.  As more and more unqualified persons do this injection, the more issues and complaints you will see.
So you need to  make sure that you see a board certified plastic surgeon for you injectable needs.

The advantage of Dysport over regular Botox is that it takes affect faster and may last longer and spreads a little more to cover more creases than regular Botox but that may also cause some more heaviness to the eyebrows for 2-3 weeks if it gets too close to the eyebrows. Neither should have much effect on the eyelids at all as far a drooping goes.