Need help in model selection

I am training mulitple pretrained models from torchvision on my own dataset. The performance of two models have caught my attention. The first model has a normally decreasing training loss and a increasing accuracy but its validation loss decreases and then keeps on decreasing but giving a bit better validation accuracy than the second model, which has a decreasing training loss and a increasing accuracy(albeit much lower than first model’s) but has a decreasing validation loss and improving validation accuracy(but still lower than first models).
How do I go over choosing which model to work with further? Do I keep training for more epochs?

Usually you would select the model yielding the “best” performance.
However, it seems you are interested in further fine-tuning or optimizing the model, so it’s a bit hard to tell, which model you should select.
Note, that the second model might learn a bit slower due to non-optimal hyperparameters, so you might want to experiment with changing these.

You could train the model as long as the training and validation losses decrease by a significant amount.

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