"Do I have a legal case?"
Depends. If you signed an actual CONTRACT then yes you might have a case for detrimental reliance and breach of contract.
"Can I pursue reimbursement of the value of the other stock I left behind under detrimental reliance and a breach of contract."
If it is actually a contract. If it is only an offer letter then you may be completely hosed. You will have to take the document to a NY attorney to see whether they can be held to it's terms. Only skilled counsel can tell you. Generally employers are free to deviate from the terms of offer letters, contracts no.