Logic would seem to dictate that if you have an agreement with someone, and the other side fails (miserably, perhaps) to live up to their end of the bargain, that you have a strong breach of contract claim.

Under New York law, that isn't always the case.
Perhaps the most glaring exception to the general rule (that it would yield a viable breach of contract claim) is in the malpractice context, particularly in the legal malpractice realm. In those cases, New York's courts have held that
"[I]t is well established that an action for breach of contract, negligence and breach of fiduciary duty are duplicative of a legal malpractice claim, as all claims arise from the same set of facts and seek the same damages, and therefore, should be dismissed. (Laruccia v. Forchelli, Curto, Schwartz, Mineo, Carlino and Cohn, LLP, 295 AD2d 321; Mecca v. Shang, 258 AD2d 569).
As a practical matter, this also means that if you lose on one of the legal theories of liability, that determination may effectively preclude your ability to proceed on the other theories that arise out of the same set of facts.
Here's why:
"[A]s a general rule, once a claim is brought to a final conclusion, all other claims arising out of the same transaction or series of transactions are barred, even if based upon different theories or if seeking a different remedy" (Breslin Realty Development Corp. v. Shaw, 72 AD3d 258).

The moral of the story? If you're going to take a shot in litigation, make it count; you may not get another chance.