Encryption mechanisms can be used to achieve specific outcomes:
- Making some data illegible, with the ability for specific individuals to retransform it into a legible format later: this can be used to implement confidentiality within some technical limitations
- Providing an authentic signature related to a specific blob of data: this can be used to provide non-repudiation in some architectures (e.g., a file upload service may require a signature whilst uploading, as a means to identify the person who uploaded the data)
- Complex architectures can be built around public-key cryptography and zero-knowledge cryptography to implement all sorts of applications such as e-voting, secure IM, authentication of websites, but that's unrelated to access control
One of the main interests of cryptography for security is that you can use cryptographic primitives to enforce some properties on data regardless of where it is being stored. One needs access to keys or needs the ability to perform very complex (allegedly, too complex to be performed fast enough) mathematics in order to manipulate encrypted objects.
Access control mechanisms primarily implement protections on the integrity and confidentiality of data. Access control requires a trusted reference monitor that enforces a policy onto data objects. Policies can either be discretionary in which case the owners of each data item (as identified by the reference monitor) decide on whom can access their data; mandatory in which case the reference monitor's administrators decide who can access what; or a mixture of the two.
What's important is that the reference monitors checks all accesses to objects against the policy. So, access control is only appropriate within systems that you control.
Access control requires both authentication and authorisation. Authentication allows you to provide accountability, meaning that you know which principal accessed which resource; this would not be possible if you encrypted data and shared a secret key between more than two individuals.
In conclusion, encryption and access control have different applications, and enforce different properties, with different scopes of applicability. They're so different that it doesn't really make sense to compare them...
Even though both encryption and access control could enforce confidentiality, encryption will only do so as long as the encryption key you used is not stolen, whilst access control will only do so as long as the data is stored and accessed within the boundaries of the reference monitor.
It is very common to combine both methods for file storage. A drive will be encrypted to avoid unauthorised accesses via the hardware (where no reference monitor may be available), and an operating system acts as a reference monitor to perform access control checks that ensure software accesses respect a desired policy.
TL-DR: Encryption produces data representations that embody properties wherever these data are stored; whilst access control enforces arbitrarily complex properties and policies, but only on systems that one controls.