Start from a key pathology principle: follicular adenoma and follicular carcinoma share the same bland follicular cytology, so what separates them is not how the cells look but whether the tumour has breached its boundaries.
Malignancy in this pair is defined architecturally by invasion. A follicular carcinoma shows transcapsular invasion (tumour pushing all the way through its fibrous capsule) and angioinvasion (tumour within vessels of the capsule or beyond). An adenoma, by contrast, sits entirely within an intact capsule with no vessel involvement.
This is why aspiration cytology alone cannot call follicular carcinoma; you need the whole resected nodule to inspect the capsule and the peripheral vessels under the microscope.
The remaining choices are unhelpful: mitotic activity, nuclear pleomorphism and tubule formation do not reliably separate the two, and the special nuclear changes that pathologists rely on (ground-glass nuclei, nuclear grooves) point toward papillary rather than follicular carcinoma. Hence the discriminating feature is invasion of vessels.
\[\boxed{\text{Vascular invasion}}\]