Aside from personal preference, is there any reason why I would want to buy a "1/4 turn" water supply valve instead of "multi-turn valves"? Is one technology/design clearly superior than the other in terms of reliability? Or is this purely just a style preference?
Yes, ball valves or quarter turn valves tend to be more reliable than globe valves. Globe valves require a washer and a tight friction fit between the seat and washer, and if either of these wear out (which they do over time), leaks start. Ball valves are much simpler in construction.
A downside to ball valves is that they are more difficult to get variable flow out of and are best when you need either on or off states, but nothing in between.
While there are more considerations for industry-specific applications, around the house, ball valves would be my choice for any shutoff valve.
I just had a problem with mine: when I turned on the 1/4 turn valve after the winter, it would not turn off completely, dripping slightly. I tried to take it apart, but it did not completely apart. In the process of taking it apart, I think I spun the plastic gate around several times in trying to remove it. I would not come out, so I put it back together, and looked into unsoldering and replacing it. However, the next time I disconnected the hose that had a sprayer on it, stopping the water from leaking out, the valve was no longer leaking. Given that experience, I would never install a 1/4 turn valve that cannot be repaired.