One of the most commons reasons that employers sue their former employees for violation of a non-compete is where that employee supposedly uses "inside information" that they gained on the job to compete with the employer.
Here's the cold, hard truth about those kinds of claims, however: Most of them will fail - at least under New York law.
There are relatively few types of information that are actually protectable.
New York's courts have articulated this rule as follows:
"That which constitutes a trade secret has been defined as a formula, pattern, device or compilation of information which is used in one's business and which gives the owner an opportunity to obtain an advantage over competitors who do not know or use it (see Ashland Mgt. Inc. v Janien, 82 NY2d 395, 407, 604 NYS2d 912 ; see also Restatement of Torts § 757, comment [b]). An essential requisite to legal protection against misappropriation of such a formula, process, device or compilation of information is the element of secrecy. Secrecy has been defined in accordance with the § 757 Restatement of Torts as: (1) substantial exclusivity of knowledge of the formula, process, device or compilation of information; and (2) the employment of precautionary measures to preserve such exclusive knowledge by limiting legitimate access by others (see Delta Filter Corp. v Morin, 108 AD2d 991, 485 NYS2d 143 [3d Dept 1985])."
In other words, it really needs to be secret.
Consequently, unless the employer can prove the former employee used fraudulent methods, such as copying of the employer's customer lists or files, chances are this specific type of claim will ultimately fail, because an employee's knowledge of a business's inner workings are not protected; nor, for that matter, is a customer list protected, provided that it could be regenerated using publicly available information.