As one who has owned and used Leicas occasionally over 40 years of shooting, with lenses from 15mm to 135mm, and with and without power winders, the following are my comments on why I enjoy shooting Leicas so much. Almost all my Leica shooting was black-and-white; I can't comment on color aspects.
1. Bulk. The Leica body is about half the bulk of a Nikon F when you actually pack it in your kit, and a little lighter. The lenses are about half the bulk of the same focal length and f/ number (though the fast tele lenses approach the size of the fast Nikkors). A full Leica kit with motorized M4 or M6, 21mm, 35mm, 90mm, can fit in the same space as a Nikon with one fast lens.
2. Distortion. Now that we have Photoshop this is less important, but in the old days, the rangefinder wideangles had significantly less distortion than the reflex wideangles. There was no easy way to correct this distortion. There's a big change from the 21mm Super-Angulon to the later lenses in distortion. (My 21mm Nikkor had low distortion too, but no advantage of reflex viewing.) This began to change when Leica put light meters inside the camera - the meter system required more separation between lens and film plane, and Leica started using retrofocus designs even in its rangefinder wideangles wider than 35mm. When the 35mm Summicron was redesigned, the new lens had more distortion than the older designs. Even a subtle amount of distortion can change the appearance to the eye - I think the mental impression of sharpness even changes when the 90-degree angles become slightly wider. I think the attempt to increase sharpness across the entire field also resulted in designs with more distortion.
3. Image quality. The Leica fast lenses were exceptionally sharp and contrasty compared to reflex lenses. Comparing my 35mm Summilux (the little one from the 60s and 70s) to the 35mm f/1.4 Nikkor - the Leica images at f/1.4 were sharp and contrasty while the Nikkor images seemed hazy by comparison. Stopping down, the lenses both improved, but the Leica always seemed crisper.
4. Focusing wide lenses. The depth of field of wide lenses, even fast ones, makes them hard to focus on the ground glass of reflex cameras, particularly in dim lighting. The rangefinder of the Leicas by contrast is easy to focus in dim light, and for wideangles is much more precise than needed to achieve sharp focus. No contest.
5. Quiet. Until the F100, which substantially quieted the Nikon shutter and mirror operation, the Nikons were much louder than the Leicas. You can barely hear the soft "schluck" of a Lieca shutter more than a few feet away unless it is very quiet. The snap and crash of a Nikon shutter and mirror is much louder and sharper. The F100 is still much louder than a Leica, but substantially quieter than the F, F2 and F3.
6. Viewfinder frame wider than the lens field. Having the bright frame and seeing outside it is great for action shots and anticipating what's going on outside the frame.
7. Uninterrupted view. You always see the image in a Leica, and you see the image the instant of the shot. With reflex cameras, it's the precise instant of the shot that you CAN'T see. What did I get? That's an issue.
8. Camera vibration at slow shutter speeds. The Leica was easier to get good available-light shots with at 1/15 or 1/8 second because of the smaller amount of camera mechanical vibration. At 1/4 and slower, I think they're probably equivalent, because your ability to keep the camera fixed overshadows any camera-caused vibration.
1. Parallax. The 2-inch separation between the finder and the lens axis is important in shooting architecture and interiors, and shooting close to the subject. It's generally not critical for reportage. In only a very few instances was this a problem for me in using Leicas.
2. Shooting rate. Even with the power winder, Leicas don't provide the high frame rate of the Nikon.
3. System range of capability. With reflex viewing, the system becomes much more capable, expanding to photomicrography, macrophotography, long telephotos, etc. No comparison.
4. View of depth-of-field effects. The reflex allows you to view directly the effects of depth of field, if you use this capability. The view is different than the print, but with practice the print view can be anticipated. With a rangefinder, you're seeing everything sharply, so you have to anticipate depth of field effects from experience.
5. Autofocus. Not available on Leica or other classic rangefinder cameras. There is nothing to prevent a modern rangefinder camera from having autofocus, but you start losing the advantages of compact size and light weight.