I wore digitals for a couple of decades and when it comes to precision timekeeping, they cannot be beat. Quartz is very accurate and a digital watch can be referenced to a standard daily in under one minute. A radio-controlled digital or even an analog will do that for you.
However, the advantage to analog for me is that they are so hard to set precisely and the analog scale, although it can be precise, is given to imprecise readings when they are simply glanced at for the time.
In this way, the analog watch helps to dampen my obsession and I am less inclined to set them each day because it is so time-consuming and because when I read the time more often than not, I am only getting an approximate reading anyway.
Today, I own 14 analogs and only one digital and it is a radio-controlled solar G-Shock.
Whereas before, I would set my watch every day, now I am satisfied to set my 13 non-radio-controlled quartz analogs every couple of months without undue emotional stress.
It still thrills me though that my G-Shock is always there and alway within .5 seconds of UTC and on any given day, which is rare, I can wear that watch and at a glance tell the near exact time.