Personally I like following best:

Beides ist gleich gut.

The word "gut" rates both possibilities as good options which does not overrule the other. I impress that I have thought about these options. In contrast if I simply say I don't care I express that I have no interest in either option and I probably have no fun in doing either.

However the difference is really subtle and it is always a matter of pronunciation and context how you say: "Ist mir egal."

Personally I like following best:

Beides ist gleich gut.

The word "gut" rates both possibilities as good options which does not overrule the other. I imply that I have thought about these options. In contrast if I simply say I don't care I express that I have no interest in either option and I probably have no fun in doing either.

However the difference is really subtle and it is always a matter of pronunciation and context how you say: "Ist mir egal."