1. Amazon Fresh prices one year ago were pretty high, they have driven costs down on everything except produce.
2. I live close to a City Target and have been avoiding Amazon Fresh because I thought the target was cheaper. Yesterday I took my $100 grocery bill and recreated it on Amazon Fresh, and excluding produce, it was $89.00. I was shocked to see the prices were cheaper for most things.
3. The delivery is free for $100 purchases, so you can't use it like regular amazon (or amazon prime).
4. The delivery times range from 5 am in the morning to late in the evening.
5. The packaging is often reuse able, plastic containers or clothe-bags and so you can leave outside and the delivery folks will pickup the old packaging, this is much more sustainable than regular amazon cardboard packaging.
6. Living in a city, it is easier and cheaper to buy in bulk of Amazon Fresh, because they prefer selling in larger quantities. Some items have 2 or 4 quantity minimums. If you don't have a car this is fantastic.
Or, if you buy enough (not entirely sure what the threshold is) to get "Big radish" status, delivery is free for $50 purchases.
The UI wasn't as good as a supermarket shelf, and Amazon didn't always give unit prices ($/lb) in consistent units across the board. I don't think they let me sort cereal by unit cost either.
At budget pricing, it didn't seem to compete with Safeway. The minimum orders needed for free delivery also tended to price out a single grad student. Re-checking prices recently when ordering for two, it seemed like it was kind of a wash.
It's worth checking out. If it works for you, it can be great.
The real win for Amazon is the upsell. If you're ordering groceries, you can also order electronics with nigh instantaneous delivery for free. It's powerfully addictive (so powerful, in fact, that I noticed and quit).
I welcome Amazon groceries.