I think it all depends how "correct" one wishes to be. I have a lovely Omega tank watch. Gold case, black strap. Certainly it's a more "correct" dress watch.
However, I won't hesitate to wear a chronograph with a suit...sometimes the rugged look of the watch is a nice counterpoint to the formality of the suit.
The Moonwatch, on me, is just a touch large to glide easily under French cuffs, though. I've got a 39mm Speedmaster Day Date that fits better in this regard, and has a "dressier" appearance.
The Day Date, like some of the chronos posted in this thread lies in the middle of that spectrum with "tool" or "sports" watches at one end and "dress" watches at the other.
The Moonwatch is farther along that spectrum towards the tool watch end...but, it's a fine, classic watch and so I often wear it with a suit...and I'd even wear it with a dinner jacket, if I felt like it, particularly now that it's on a black crocodile strap.
All fashion, watches and jewelry are elements of personal style, and to each his (or her) own...
Here's that Day Date Speedmaster...