As someone that has shop that both supermarkets I feel Stop & Shop has better deals at times but don't take my word for it, try it yourself shop at both places and see which one works best for you...
The deals vary from week to week. Check weekly circulars and compare the deals of the items you are interested in.
Amazon
What a subjective question, it mainly depends on what specially you are looking for deals on. I'd say Stop & Shop overall, but that's just my opinion - I don't shop at Shop Rite all that much for a proper objective comparison.
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