This is a good question. The naïve view would be that there is no difference besides "there just being more images". However, this is not necessarily the case.
The answer depends on how "true" your augmented dataset is to your original dataset. In some cases, the augmentations are less representative of the original images. In that situation, not including the original dataset in your training may be harming your training/model performance more than "there just being more images". You would also influencing the quality of your training.
In some cases, you can tell a priori if the augmentation is representative of the original. For example, a a car vs. truck dataset that is flipped horizontally is probably representative of the original.
In situations where you cannot tell a priori, you can train a model with the original dataset and another model with an equal number of augmented images. In situations where the augmentation is "true", there should not be a huge difference in model performance. (With small datasets, the fluctuations in performance can be "huge", and this would not apply).