Thank you Alex for your reply!
After some inspection I realized that the R2U-Net has around 6 million parameters compared to vanilla UNet which has 1 million parameters. So in a mathematical sense a more complex model results in a curve which fits the training data points perfectly and does not generalize well to unseen data.
Early stopping would imply I am settling for an inferior model performance. If I want to improve the model performance I would have to opt for regularization and more data. Is this conclusion right?