There are various (very pricey) commercial response boxes or pads (perhaps most notably Cedrus) that purportedly offer higher precision than regular keyboards. (Note that my question focuses on precision, not on accuracy, though similar doubt applies to the latter too.) However, I cannot find any study (peer-reviewed or not) that verifies this. Instead, I find studies that show that regular keyboards are very precise anyway (e.g. this, showing max 3-4 ms standard deviation). In any case, is there any actual evidence out there for better precision with dedicated commercial hardware?
It all depends on what you wish to measure; if you are after measurements where a few milliseconds matter, response boxes are the way to go.
RT measurements are finicky; USB peripherals add polling latencies to your recorded response times. This can add unacceptable latencies (8 ms or so) to RT estimates. Apart from this effect on accuracy, graphics latencies in visual tasks, or syncing issues in auditory-visual tasks can seriously mess up the stimulus timing. Further, first-time calling of MATLAB commands are notoriously sluggish and they may add unacceptable latencies to the first trial. MATLAB in general is also notoriously bad in controlling exact stimulus timing; it's simply not designed for this type of experiment.
Windows in general is a platform not suited well for real-time operations, because it maintains its own agenda in terms of which process is run first in the cue, this may be virus scanning, updating, or your reaction time experiment. Since different operations in the queue may add different delays in your experiment, trial-to-trial errors are introduced with variable magnitudes, messing up your precision. Mac OS is better, and Linux beats them both in terms of exact timing control.
The Psychophysics Toolbox help site and associated user forum have a wealth of information on these things.
Response boxes solve these issues, because the time stamping is controlled by the hardware inside the box, taking the load of all the timing processes away from the pc. This substantially reduces latencies (hence improving accuracy) and takes away much of the variability as well (hence improving precision).
But everything depends on the type of reaction time you are after. Are you interested in millisecond-range responses (standard react as-fast-as-you-can tasks), or do a few seconds more or less not matter (tasks where subjects get the time to make a cognitively evaluated choice)? In the former, response boxes are the way to go, in the latter it all really doesn't matter and a keyboard or a mouse will do the job just fine.