The concept of overfitting does not generalize over a specific combination of batch size and epochs. It depends on your data and the architecture of your model
A friend of mine ran into these scenarios with a CPU based image classifier:
1) If I use more epochs ,it may take me a lot of time to come to a desirable
2) If I prefer small batch-sizes over small epochs , It might take less time
time to compute , but not reach the desirable outcome by that epoch limit.
I used a GPU and my results were different. Using low epochs , and better convolutional architecture , I reached a better accuracy with not so small batch sizes.
I increased epochs, and my accuracy improved until I felt I reached overfitting.
I increased batch-sizes and my accuracy was not increasing at a decent rate.
I had to come to balance at which my model was acceptable.
Its a balance , yes. A balance which I am afraid, the designer needs to take care of. Not always they are inversely proportional. The data set and the architecture makes all the difference in this debate I am afraid.