This is really an apples and oranges comparison: They are not the same thing...
A good carabiner will have a rating on it that is specified in kN, Kilo newton, or Newtons of force. The idea behind a carabiner is that if a person falls off a cliff and accelerates with gravity, they will generate a great deal of force when brought back to rest by the carabiner.
The carbiners I have used were all designed with two things in mind:
First, they will bend and flex when put to the test of stopping a person, and if used repeatedly will break.
Second, all carabiners are to be replaced if subjected to that type of fall or flexion.
If you can imagine a boat at anchor, bobbing in the swells, you are essentially placing repeated strain on the carabiner, which is something they are not designed to do.
In the case of small boats, there isn't much to fault the carabiner, it would likely hold a 3,000 pound boat in a steady breeze and small swell without a problem. However, if we get into anything heavier than that, I'd be very reluctant to use the carabiner.
Another point about carabiners is that it is possible to purchase the non-climbing type without knowing what you're buying. They're everywhere and even if it had a lock mechanism, you could possibly be buying a carabiner that is os questionable quality.
My final point about carbiners, is that they are far more expensive than a shackle. In fact REI is asking $9.50 for the basic Omega screwgate carabiner. I can get 3 or 4 1/2" shackles for that price at the store.
Here's a good report on anchors, hope it helps:
Catenary & Scope In Anchor Rode: Anchor Systems For Small Boats