We stayed on Rendezvous Bay when in Anguilla and the water was neither clear nor calm. I loved the island but we just happened to hit a windy week and there were days when we could not be on the beach because of stinging sand. The water on Shoal Bay was much closer to what the OP described. That being said, I still prefer the water and beach in Negril to Anguilla.

After all the discussion about what constitutes REALLY clear, placid water for beaching purposes, I will say that Anguilla doesn't make my top 5 list for this particular characteristic. Turks, Bahamas, Cayman etc would be on that list.
That said, I prefer Anguilla over each of those islands as an overall vacation destination.

"Clear and calm" is always subject to weather.

We were looking forward to those adjectives on our first trip to Provo, but lo and behold, a tropical storm passed nearby (in December!) and Grace Bay was kickin' up a ruckus.

Conditions can vary a lot at Negril, too.

This is why I like the Virgin Islands (e.g. St. John, Virgin Gorda, St. Thomas). There are lots of nice small beaches in protected bays, and if the wind picks up from one direction, you can hop over to the other side of the island.

Oh my goodness! Now I'm more confused than ever! Maybe somewhere in the South Pacific would be better in August??