<p>That is because of the Mini-batch gradient descent effect during training process. You can find good explanation <a href="https://machinelearningmastery.com/gentle-introduction-mini-batch-gradient-descent-configure-batch-size/" rel="nofollow noreferrer">Here</a> that I mention some notes from that link here:</p>

<blockquote>
  <p>Batch size is a slider on the learning process.</p>
  
  <ol>
  <li>Small values give a learning process that converges quickly at the
  cost of noise in the training process.</li>
  <li>Large values give a learning
  process that converges slowly with accurate estimates of the error
  gradient.</li>
  </ol>
</blockquote>

<p>and also one important note from that link is :</p>

<blockquote>
  <p>The presented results confirm that using small batch sizes achieves the <strong>best training stability</strong> and generalization performance, for a
  given computational cost, across a wide range of experiments. In all
  cases the best results have been obtained with batch sizes m = 32 or
  smaller</p>
</blockquote>

<p>Which is the result of <a href="https://arxiv.org/abs/1804.07612" rel="nofollow noreferrer"><strong>this paper</strong></a>.</p>

<p><strong>EDIT</strong></p>

<p>I should mention two more points Here:</p>

<ol>
<li>because of the <strong>inherent randomness in machine learning algorithms</strong> concept, generally you should not expect machine learning algorithms (like Deep learning algorithms) to have same results on different runs. You can find more details <a href="https://machinelearningmastery.com/randomness-in-machine-learning/" rel="nofollow noreferrer">Here</a>.</li>
<li>On the other hand both of your results are too close and somehow they are equal. So in your case we can say that the batch size has no effect on your network results based on the reported results.</li>
</ol>
Why does different batch-sizes give different accuracy in Keras?
<p>I was using Keras' CNN to classify MNIST dataset. I found that using different batch-sizes gave different accuracies. Why is it so?  </p>

<p><a href="https://i.stack.imgur.com/Ad4oO.png" rel="nofollow noreferrer">Using Batch-size 1000</a> (Acc = 0.97600)</p>

<p><a href="https://i.stack.imgur.com/CRLd3.png" rel="nofollow noreferrer">Using Batch-size 10</a>  (Acc = 0.97599)</p>

<p>Although, the difference is very small, why is there even a difference?
<strong>EDIT - I have found that the difference is only because of precision issues and they are in fact equal.</strong></p>