Both types of boots have there disadvantages and advantages depending on the terrain you will find yourself in on your next hike. Ankle support hiking boots are great if you are going to find yourself in a terrain that is off a path and you will find yourself walking through a thick bush. The ankle support will help when stepping on uneven ground and also protect the ankles from sharp thorns or plants that can cause cuts or scrapes.
If you will be finding yourself on a hike that is on a path or flat ground, you will most likely want a pair of boots without ankle support as they will help you to be more mobile and fit better, and you will not need the extra protection from backcountry bush.
Either way, both types of boots are great and will give you the protection you will need to complete your next hike.