If the training accuracies are similar then their testing accuracies (accuracy on test data) must be checked (one can also use cross validation). Moreover, another choice could be looking at the other performance parameters like Precision, Recall, r2 score, MSE, etc. and then choosing the best model. However, if still most performance parameters matches, one can choose a smaller and more computationally efficient model.

I would consider the following:

The question just doesn't make sense, since ``best'' hasn't been defined beforehand. If ``accuracy'' is the only feature and both models score the same, this just means that it's not possible to select one over the other and which one is used is a matter of taste.

Try to test them on more precise data, or on data taken under different circumstances (higher temperature/pressure, humidity, tension ... )

Besides the accuracy the adequity matters too. In case of statistical modeling, say regression or Kalman filtration, the residuals been obtained are to be casual, independent and distributed due to normal law values . For the first thing people uses a turnpoint criterion, for the second one - an autocorrelation function, and for the third one - X^2- or Kolmogotov- Smirnov or Johnson- Darling criteria.

Morover, You should choose the adequate model with worse accuracy if the model with best accuracy is not adequate. Voila!