For the type of stuff they do at Carderock, I'd say experiments are way better. Maneuver dynamics is really, really hard to do, as the time scales of the problem are long (ships turn on the order of a minute), something very challenging for CFD to accurately represent. Also, accurate free surface liquid dynamics is really damn hard to do, and I'd be skeptical of of most model's accuracy. I certainly wouldn't make billion dollar decisions on it.
In aerodynamics, which has had much more time and money invested, CFD can almost completely replace the wind tunnel, but only for aerodynamics problems we understand (ie wings, fairings, nacelles, turbine blades, backward facing steps, etc). As soon as you leave the validated/understood world, CFD becomes a tool used to augment the designer's intuitions, with the wind tunnel providing an essential ground truth.
Fluid dynamics is the business of predicting complex nonlinearities to a few %, and imo, complex nonlinear models are only useful when validated.
It's telling that when they debated building the DDG1000 they built a 1/4 scale ship:
I'm hoping someone with recent experience answers your question. I worked at Carderock in the early 90s, and I can tell you then, computer models worked only for the simplest shapes (only underwater vehicles, nothing on the surface) and were used to narrow down the number of physical models, but the computer models were nowhere close enough to real world to be used in place of extensive scale models.
of course, the phone I am writing this on probably has more processing power than the cray I was using back then!
I'll add that it is not just processing power that is the issue. The Navier Stokes equations for fluid flow (and the related equations) do not have closed form solutions. And even if they did, there are observed flow phenomena that cant be captured. CFD is an area where our mathematical understanding of the problem needs to advance further before we can accurately model in silicon. Some incredibly fascinating problems there - I sometimes wish I had stayed in the field.
I can say, with some exposure to the issue through my own work, that as time passes CFD modeling, mostly in the form of numerical differential equations played out in a supercomputer simulation, is rapidly replacing physical models, partly because computer modeling is becoming less expensive, and partly because one can try more design variations in a shorter time than one can with real models.
CFD is improving at great speed, along with the increase of computer power, but isn't yet in the level required to replace all scale model tests and they can still be very computer intensive. I guess that nowadays the state of the art are these new Smoothed-particle hydrodynamics models. I've worked with basins like that to test harbour and breakwaters designs and I can tell that it is common and good practice to test breakwater designs in scale models before being built, there are too many variables and hydrodynamic process (like turbulence, porous media flow, wave breaking, over-topping etc..) that cannot yet be reliably modelled using CFD, specially when they cannot be simplified to a 2D domain. Nonetheless there are types of scale models that are increasingly rare these days because they were replaced by CFD modelling, like sediment transport, although they were/are pretty cool to watch. Also scale models are very useful to calibrate CFD models.
