First of all, what you are talking about is "access" not "scope".  It is important to get the terminology correct.  Scope has a different meaning in Java.
An abstract class is really just like a normal class with normal implementation details (state variables and code) ... except that some of the implementation is left out; i.e. the abstract methods.  So naturally you want the full repertoire of class language features.
A (pre-Java 8) interface is different1.  Now there is no state and no code, just a "contract" that any implementing class must fulfill.  
Now that doesn't completely address this question, but for the rest, I refer you to this Q&A - Protected in Interfaces - which asks why you can't use protected in an interface.  As you can see, there isn't a single convincing answer.  Rather there are multiple answers proposed, each of which could be valid to a lesser or greater extent.  The only way to get the real answer(s) would be to ask James Gosling et al.  Ultimately, it was a design choice made early in the life of the Java language.
So, why different rules for both?
Because the purpose of each of the two constructs is different.
1 - With Java 8, we can now declare default methods in an interface.  In other words, there can be code in an interface now, albeit code that is common to all classes that implement the interface.