Are "1/4 turn" water supply valves more reliable than "multi-turn" valves? Or vice-versa?
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.