Set difference of recursively enumerable language and regular language

Consider a recursively enumerable language L1, and a regular language L2.

Is L1\L2 regular, context-free, or recursively enumerable?

Is L2\L1 regular, context-free, or recursively enumerable?

My thought process is that L1\L2 is recursively enumerable and L2\L1 is regular. Is this correct?