Which is more important - stable training results or good test results?
I would personally prefer the scenario where the training/testing accuracy is high/low respectively, because it would mean that your model was at least well-fit in the training data but unfortunately performed poorly on unseen data. It is also a conservative scenario, because it can't get worse than that, so you have a good feeling that your model needs improvement.

On the other hand, if your training accuracy is low, you shouldn't even test the model on unseen data, because you are certain that it is not trained well enough. However, if you insist on testing it, even though the training accuracy is low, and the testing results are better than the training results, then this probably means that you were lucky during testing. Under no circumstances should you make any inference of the model's quality in such a scenario.

The solution to your problem would be to use k-fold validation, meaning that you should randomly split your dataset multiple times into different training/test sets and evaluate its training/testing accuracy over all the splits to have a better feeling of how the model behaves on your dataset.