I can't really think of a context that this phrase could be used where it's the same meaning as мне все равно. I think that'd be "Whatever you want" rather than "Whatever you say".

In one context it usually comes off as а snide remark, it's like saying "I still think you're wrong, but I'm done arguing." Sometimes people just say "Whatever". It's usually used by someone to try and have the last word without actually saying anything of substance, hence it coming off as being snide (in the sense of насмешливый, I think).

In another context, like kybarry said, it can imply you don't believe what the other person is saying. In this context it can be snide such as in the other context, but it can also just be said in a teasing manner.