When picking a single note at a time, using the flesh of the finger makes a softer sound than using the nail, just like when strumming. I don't think there is a right or wrong technique, you just use whichever depending on what sound you want to get, and you practice it over and over again to get that sound in a consistent way so you're more in control. Personally, I like picking with the flesh of the thumb when playing something a bit jazzy and smooth, then picking with the nail if I want a more precise or more aggressive sound, and often I mix the two and use the index finger as well (I never use my middle and pinky finger, maybe I should?). From what I've read on this board, how you shape your nails when you cut them changes the sound as well, but I'm not taking it that far. Keeping my nails short on my left hand is enough of a manucure aesthetics trauma for me as it is lol
A lot of people strum or pick the strings where the fretboard meets the body of the uke or higher up. I tend to do it lower but I have no idea why I do it this way and whether it makes a difference or not. Then there's how rigid your finger is when you pick, what movement you do with your wrist, what angle you pick the strings at etc, all of this changes the sound too. Quite hard to explain by text and not sure I've gotten it right so...
I remember Aldrine had Uke Minutes about how to pick strings in different ways to get different sounds, maybe have a look at the video in the archives to get a better sense of what I'm on about?