FNAC is useful in all the following types of thyroid carcinoma except -
"FNA biopsy is unable to distinguish benign follicular lesions from follicular carcinoma. Therefore, preoperative diagnosis of cancer is difficult unless distant metastases are present. Large follicular tumors (> 4 cm) in older men are more likely to be malignant." - Schwartz Surgery
FNAC is the investigation of choice for solitary thyroid nodules.
It cannot distinguish between a Follicular Adenoma and a Follicular Carcinoma as this distinction is dependent not on cytology but on histological criteria such as capsular and vascular invasion. It thus cannot be used to diagnose follicular carcinomas.

Note here that -
The criteria for vascular invasion is applicable only for capsular vessels and vessels outside the capsule. the presence of tumor plugs within intratumoral blood vessels has little prognostic significance
Papillary
Follicular
Anaplastic
Medullary