I've used them both, in my opinion the one with laces (#2) is better in every possible aspect. Way better support and fits much better into the skate.

However I strongly recommend doing as much rehab as possible at the same time. With those braces ankle muscles can go pretty bad. Every last piece of ligament was torn inside my ankle in a soccer injury but I was able to rehab it 99% in the end and no need for ankle brace anymore. The younger guys already call me the Robocop so getting rid of one brace was nice.

Edit: The stabilizer I have is that Mueller, it felt really bad in a skate since it's quite thick. The laced one was this model to be exact. I used it without those plastic things in a skate and the fit was good with very strong support. The Mueller's laced brace is probably equally good.