Is there a way to recognize which of these scatter plots is "better"?
You could:


Label manually few of them (say 100-150), then train a simple model to classify data. A small Random Forest could do the job well.
Train a super basic model on the each dataset used to produce each scatterplot. Something like a Linear Classifier. If the Classifier doesn't make mistakes, you have "clearly separated data", if it makes mistakes then it's likely to be the opposite.