Fine needle aspiration cytology (FNAC) entails using a narrow gauge (25-22 G) needle to collect a sample of a lesion for microscopic examination. It allows a minimally invasive, rapid diagnosis of tissue but does not preserve its histological architecture. FNAC is commonly used for diagnosis of breast cancer, with traditional practice being based on the subjective visual assessment of the breast cytopathology cell samples under a microscope to evaluate the state of various cytological features. Therefore, there are many challenges in maintaining consistency and reproducibility of findings. However, the advent of digital imaging and computational aid in diagnosis can improve the diagnostic accuracy and reduce the effective workload of pathologists. This paper presents a comparison of various deep convolutional neural network (CNN) based fine-tuned transfer learned classification approach for the diagnosis of the cell samples. The proposed approach has been tested using VGG16, VGG19, ResNet-50 and GoogLeNet-V3 (aka Inception V3) architectures of CNN on an image dataset of 212 images (99 benign and 113 malignant), later augmented and cleansed to 2120 images (990 benign and 1130 malignant), where the network was trained using images of 80% cell samples and tested on the rest. This paper presents a comparative assessment of the models giving a new dimension to FNAC study where GoogLeNet-V3 (fine-tuned) achieved an accuracy of 96.25% which is highly satisfactory.