I have used both apps (calm and headspace) for over 2 years now and I would say headspace is more structured. Calm offers very good theoretical content, the app itself has a nice interface but if you start one of the packages (such as calm for anxiety or calm for sleep) it throws a good amount of information at you only in less than a month. That means you learn the theory but don't have much time to actually practice it.
Headspace on the other hand has a very well structured set of diverse packages that you can do after finishing the basic packages. You get to learn the theory really well and then have a very laid back approach in implementing and practicing concepts.
Using the unsubscribed versions of both apps, you can only acquire an insight into meditation.