One reason to choose pure abstract over interface is to force sub classes to implement particular methods that are implemented by a super class.
For example (in Java),
Say you want all extending classes to implement toString(), equals(), and hashCode().
You could create an interface called ForceSomeMethods for that contract, but those methods are implicitly implemented by Object.
Making ForceSomeMethods a pure abstract class with toString(), etc as abstract methods, all subclasses will be forced to implement those methods.