My sense is that "pick out" means that the group is tangible and right in front of you (all the options are physically together) and that is a fairly objective choice.
- e.g., He picked out the tallest guy in the police line-up.
- e.g., He picked out the biggest piece of cake
When the choices are spread out or more abstract or subjective, I would never use out.
- e.g., He picked the best place to live (but had to go to different houses in different neighbourhoods on different days and then compare them. In addition, someone else might have chosen differently, based on their preferences, and also picked the best for their own situation.)
- e.g., He picked the right career (given his skills, temperament, and experiences, there were likely a few different jobs that he would be very good at, and he chose well to settle on one of these (rather than from among all the others), but it was not as simple as just picking an object - he had to study this, learn that, make these mistakes and have these experiences before he could become good at his career)
- e.g., She picked the tallest guy in the neighbourhood to date (even if true - did she check every guy - she did not line them up at one time and pick him out)
- e.g., He picked the best piece of cake (all the pieces were together, but it is his or your opinion, not necessarily shared by others)
Actually, I probably would alter the first case, but that's more a personal style - using out is correct
- e.g., He picked the tallest guy in the police line-up
- e.g., He picked the tallest guy out of the police line-up.
- e.g., He picked the biggest piece of cake (out of those remaining)