I wouldn’t get all that excited. Other than being tax-free....you don’t save that much.
If you do watch for sales...like for watches, cameras, etc....you might find some exceptional deals. But on regular daily prices, there’s no real savings. I would advise to get on the mailing list with them for weekly or monthly sales, and pay attention to what is listed.
Example: I got a pair of water-proof winter boots that typically sold for $125 at the BX (would have been near the same price via Amazon), but some spring weekend sale dropped them to $75, and they still had them out on Monday morning...unsold, and they dropped them another $15 (exceptional deal at $60).
I don't know about today, but Navy Exchanges were definitely significantly cheaper in the '60s and '70s.
And Amazon is not always the cheapest either.
The problem I have with military exchanges is that they sell mostly top-of-the-line products. I don’t care how much you discount that $1500 watch it still Isn’t going to be in my price range.