What is the best way to compare various classification models? If I have two classifiers for example Neural network and support vector machine , now I want to know what would be the best way to identify which is good classifier , should it be based on classification accuracy or by analyzing confusion matrix or average precision score, f1 score etc.

I have seen in most of the papers related to image classification that they only take classification accuracy as the parameter to compare different models.
Since the problem you are trying to tacle is image classification, then classification accuracy is the appropriate measure of comparison. Also you could consider the Precision, Recall and F1 metrics (for multi-class problems). See below there is description of an extension about these multi-class metrics.

A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems  

Another appropriate metric is AUC/ROC, which has to be extended cosnidering the multi-class case. See the link below 

Receiver Operating Characteristic (ROC)