To me, quartz and mechanical are two totally different animals. Yes, they are both watches, they both perform the same function but they are very different. I might like the difference between cats and dogs. They are both house pets, yet they have very different personalities.
If you think about watches only in terms of functionality, then a quartz is no different than a mechanical, (except perhaps in positive ways- it is more reasonably price, lighter, much more accurate). If you want basically just something that looks nice and tells time, a quartz might be fine for you.
However, in my mind, I would not consider owning a quartz watch owning a watch. This is not because it is not a watch because obviously it is, and not that quartz watches are worse in some objective way (because they aren't) but because the experience I have in owning mechanical watches is so different from quartz I would not consider them the same thing at all.
If you have ever owned a mechanical watch you appreciate the 'soul' it brings to the experience of owning it. The sound of the rotor, the sweep of the second hand, the ticking sound it makes, the interaction of winding and setting a watch (perhaps using a winder), the weight of the watch, learning about the movement, understanding what goes into accuracy, servicing the watch (and perhaps doing some work yourself if you become knowledgeable enough and are so inclined), the satisfaction of investing real hard earned $ in your watch, and of course planning your next grail purchase. This is an experience that cannot be quantified by 'better' or 'worse', it is just an entirely different experience that to many watch owners is an entirely different concept than quartz.
Personally, I could not wear a quartz again on any regular basis, except maybe to paint a house, pound nails, or swim in a murky lake (and even then a low end Seiko diver could be abused for this purpose). I would clearly rather wear a $150 Seagull or Seiko than a $1500 Breitling or Tag quartz.
But, that is my experience. I suggest you decide for yourself what is for you. Consider picking up a Seagull, Seiko, or Orient and seeing how you feel about it. You can always flip these for a minimal loss if you decide it's not for you. However, if you never try a mechanical you will never know what you might be missing.