Nomos Neomatik vs Mechanical

I think you have some confusion regarding these terms. An automatic is a mechanical. The other kind of mechanical is a hand wind. All Nomos are mechanical. if it's not mechanical, it's quartz (electric) with few oddball exceptions. 

If one is wearing the same watch every day, automatic can make sense. Otherwise, I don't know why people bother with the things. Need I mention that they are trickier, and presumably more expensive, to service?

Most of my mechanical watches are automatics - the Omega Speedmaster Professional is the only manual wound mechanical I own. I tend to personally have a very slight preference for the convenience of an automatic, but the automatic winding rotor tends to add height to the watch, and can get in the way of the view of the movement for watches with exhibition case backs. Those drawbacks can be addressed with a micro rotor, but I don't have any micro rotors in my collection. The biggest potential drawback for hand wound mechanicals is that you need to remember to wind them if you wear them for more than a couple of days. I don't really have a huge preference, it just so happens that most of the watches in my collection happen to be available as automatics. 

Automatic or handwinding doesn't really matter to me. I can have it either way. Due to a relatively heavy rotation I end up winding all my mechanicals before I can use them albeit lesser winding for automatics just to get them running and the rotor does the rest. Unless maybe if I get longer power reserve autos of 8days or more like some IWC's. 😂

Depends on how many watches you own and how frequently you wear them.

If you have only one watch or two watches that you switch between, then go with the automatic as it will keep running as long as it has a decent power reserve.

Otherwise, really no difference. I always give my automatics a good 30 winds when I prep them the night before, same as what I do with my manual wind watches.

To me the biggest pain is setting the day/date. No so bad for modern watches with a quickset day/date complication. However, on my vintage watches it is a real pain. Usually I wait until the date on the watch is close to the date of the month and then I select that watch. Much less effort on setting the date.

I have no problem winding my watch if it saved a chunk of money. I enjoy it. 

I somewhat agree with the above comments about how many watches you own, because if you only own one watch and it’s not a fairly accurate one then you need to set the time every few days anyway. If I only owned a Seiko GMT with a 4r34 movement (+45/-35 sec/d) and it ran around 20 seconds slow per day then after a week you’d be running two minutes late to your Zoom meetings, for instance. 
 

But if you have a very accurate movement then you might only need to reset the watch monthly or so, and that would be fine for a one watch collection or even two if you go back and forth on a daily basis (depending on power reserve, of course).
 

I only own one hand wound movement, a Speedmaster Pro, but since I rotate between 6 watches most of the time (plus a couple G-Shocks) then the Speedy is no different to the automatics for the most part, except that the seconds don’t hack. They all get wound in the morning when I put a new watch on.