For classification accuracy, I strongly suspect model B would work better.
I’m less familiar with ranking, but I’ve gotten qualitatively good results by training with softmax+cross entropy and doing KNN on the features (the before-last layer). If you have time, you might want to try both.
https://users.eecs.northwestern.edu/~jwa368/pdfs/deep_ranking.pdf 224 looks like it uses triplet loss for ranking images.