The Nikon has 1:1 viewfinder magnification and an etched, non-parallax-compensating frameline for the 50mm field of view. The Contax has a smaller frame magnification (about 0.70x, I think) and no framelines at all -- you have to rely on the fuzzy border of the finder to indicate the edge of the image. Advantage: Nikon.
The Nikon has fast and slow shutter speeds on separate, coaxial dials; the fast-speed dial rotates as the shutter fires, meaning you have to keep your fingers clear to avoid inaccurate shutter speeds. The Contax has all shutter speeds on a single dial. You have to lift and turn this dial to set it, so it's a bit slower than a modern one, but at least it doesn't rotate as the shutter fires. Advantage: Contax.
Both cameras load via a removable back. The Nikon has a single twist lock, making for slightly faster operation than the Contax, which has two twist locks. The Nikon advances film via a thumb lever and rewinds via a folding crank; the Contax uses knobs for both operations, making them slightly slower. Advantage: Nikon.
The Contax shutter consists of vertically running metal slats; the Nikon has a conventional, horizontal-travel cloth focal plane shutter. The Nikon's cloth shutter curtains are susceptible to burning by the sun if you don't take a few simple precautions, but its overall construction is simpler and probably more reliable. The Contax shutter is burn-resistant, and when adjusted correctly it's a bit quieter, but it's also more complex and requires more specialized maintenance skills. Advantage: Tie.
The Nikon is a handsome, rugged-looking, nicely-made camera. The Contax is an exceptionally beautiful mechanism, with fantastic detail in the textures of controls and variety in the surface finishes. Advantage: Contax.
So, the basic question: Should you buy a Nikon, or a Contax? The basic answer: Yes.