The quartz vs. automatic/mechanical is an intellectual vs. emotional discussion.
Intellectually, the quartz is the superior timepiece. It is more durable, more accurate and with few exceptions less expensive. Throw in solar and atomic timekeeping or GPS and the quartz becomes even better.
Emotionally, there is a certain appeal in not having every element of your life controlled by fast-moving electrons and appreciating the excellence that can be achieved with coiled springs and gears powered by mechanical kinetic energy. The automatic/mechanical watch traces its history to the early 16th century when Peter Henlein created the first portable timepiece and there is something appealing about being a distant part of that lineage.
Both quartz and automatic/mechanical have their place in the grand scheme of things. Only the foolish would dismiss or disparage either.