Increasing accuracy by changing batch-size and input image size
If your model is a regular convolutional network (without any weird hacks), the samples in a batch will not be connected to each other. 
Depending on which loss function you use, the batch size might be important too. For regular functions (available 'mse', 'binary_crossentropy', 'categorical_crossentropy', etc.), they all keep the samples independent from each other. But some losses might consider the entire batch. (F1 metrics, for instance). If you're using a loss function that doesn't treat samples independently, then the batch size is very important.
That said, having a bigger batch size may help the net to find its way more easily, since one image might push weights towards one direction, while another may want a different direction. The mean results of all images in the batch should then be more representative of a general weight update.
Now, entering an experimenting field (we never know everything about neural networks until we test them), consider this comparison:

a batch with 1 huge image versus   
a batch of patches of the same image

Both will have the same amount of data, and for a convolutional network, it wouldn't make a drastic difference. But for the first case, the net will probably be better at finding connections between roads, maybe find more segments where the road might be covered by something, while the small patches, being full of borders might be looking more into textures and be not good at identifying these gaps.
All of this is, of course, a guess. Testing is the best.
My net in a GPU cannot really use big patches, which is bad for me...
I am extracting a road network from satellite imagery. Herein the pixel classification is binary ( 0 = non-road, 1 = road). Hence, the mask of the complete satellite image which is 6400 x 6400 pixels shows one large road network where each road is connected to another road. For the implementation of the U-net I divided that large image in 625 images of 256 x 256 pixels. 
My question is: Can a neural network easier find structure with an increase in batch size (thus can it find structure between different batches), or can it only find structure if the input image size is enlarged?