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.
The multi turn shut-off valves use a rubber washer. Over time the rubber deteriorates and gets cracked or dissolves into something that looks like black ink and the valve will no longer shut off. The 1/4 turn valves don't have a rubber washer. They have Teflon seats. The hope is that the Teflon will not deteriorate and the valve will last longer. I can't say for sure that it works because I only have a 4 ball valves installed. The oldest of them has only been in service for ten years. BTW I use compression fittings rather than solder.
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.
My house had 18 of such quarter-turn valves installed on under sink and toilet supply lines. Over time many of these developed issues - stiff, hard to turn, or completely failed to shutoff water. This happened as early as then the house was 10 years old. Now the house is 19 years old, I can count about half of these valves failed (turned to closed position and water still flows at full speed). Most of these failures happened on the hot water side which rarely get used. A few of these got replaced with the multi-turn types about 8 years ago, and these multi-turn ones still work well - no issues with stiff turns or leaks.
I had to replace a few of my stop valves for faucet repairs since I couldn’t turn the valves. I could wiggle it a little but I couldn’t turn the water off. I also noticed that the faucet had some black bits of something in them at the outlet screen. At first I couldn’t figure out what it was until I saw the condition of the sealing washer of the stop valve. The washer was starting to disintegrate. Those black bits were from the worn out washer. That’s when I decided to buy 1/4 turn all metal stop valves. I’ve seen people in videos mentioning that they were finding black bits in the catch screen of their faucets. I wonder if they had to replace their stop valve before taking apart their faucet to try and figure out the water output was low.