I completely prefer analog time (as you might have guessed). There's something so satisfying about having a mechanical watch on your wrist. Also, as you mention, analog time keeping forces you to experience time a little less precisely.
There's an analog watch that takes this concept to a whole new level, you might have heard of it—it's from a company called Slow Time:
That looks really cool, actually! I like the 24-hr part most of all.
Japan uses 24-hr time for almost everything: time-tables, schedules, any digital clocks, etc. I've long gotten used to it. Altho I have also gotten to the point where I can instantly convert from an analog clock to 24-hr time, I would love an analog clock that natively displayed 24-hr time.
On one hand, I'm very much a traditionalist in many ways. If I could find a good analog watch face for my Apple Watch that used roman numerals, I'd switch to that in a second. On the other hand, I also love new progressive ideas. Switching to that slow time would be right up my alley!
The "slow time" watches are a very cool concept. It's a shame they haven't caught on on a widespread basis. The 24hr time makes so much since to me since it eliminates the need for AM/PM. It's just way more logical.
Have you delved into the third party faces for Apple Watch yet? There are some cool ones, even reproduction of famous Swiss watches (Rolex, Patek Phillpe, etc.).