Both are correct. In the U.S., "what a pity" sounds really formal, so sometimes people say it as a joke. You can also use "what a shame," but it sounds like an older person's saying (in the U.S.). If someone else missed a good opportunity and was telling you, you can say, "I'm sorry" or "that sucks." But don't say "that sucks" to older people, because some get offended.

Both are correct. Personally, I'd be more inclined to use "what a shame" than "what a pity". Both phrases are fairly rare in the few places I've lived in the USA (Atlanta, Central New York, New Jersey). I hear it more from the elderly and from my friends raised in the UK, but it's certainly never sounded strange --- just a little uncommon in my experience.

Either although pity sounds more formal or serious to me.