For every two decidable languages There is a turing machine that decides if they are equal
Many problems that are decidable for regular languages become undecidable for context-free languages. 

Even the intuitively simple problem $L = \Sigma^*$ is undecidable for context-free $L$, where $\Sigma$ is the alphabet of the language. That of course means that equality for context-free language $L=K$ is undecidable too.