Object.freeze() seems like a transitional convenience method to move towards using const in ES6.
Are there cases where both take their place in the code or is there a preferred way to work with immutable data?
Should I use Object.freeze() until the moment all browsers I work with support const then switch to using const instead?
const and Object.freeze are two completely different things.
const applies to bindings ("variables"). It creates an immutable binding, i.e. you cannot assign a new value to the binding.
Object.freeze works on values, and more specifically, object values. It makes an object immutable, i.e. you cannot change its properties.