A different experience. Each has its own merits.
The Leica M is a no-compromise camera. It has an advanced metering and flash-meter system (the TTL models).
Whereas the Zeiss Ikon is totally battery dependent, the Leica M7 offers some manual speeds in the event of battery failure. Other M models use the battery only for the meter.
The body is one piece -- which makes it very rigid. I think it's largely brass and steel construction, which gives it considerable weight. However, a heavier camera can provide a stable shooting platform. Try handholding a plastic point-and-shoot (film or digital) at lower speeds, and you'll know what I mean.
There is a learning curve to loading the film. I think I got it down on the second try. So it's not a huge deal. The flip-up door was a worthwhile improvement to the design.
A Leica is almost a religion -- certainly it seems to generate a lot of love and dislike.
Compared with the Zeiss Ikon, it feels a bit less modern. I liked the viewfinder on my M6 and didn't seem to suffer from the flare-out of the rangefinder patch that users have mentioned.
The cloth shutter of the M6 is quieter than the Zeiss Ikon's metal-bladed unit. My only gripe about the M6 was that I felt the release point for the shutter release was too low. I like a camera that releases at about 3/4 of the way down. I felt that the M6 released at about 7/8 or nearly all the way down. I missed a couple of shots because of this. I added a so-called soft release, and I felt this made a big difference in a positive way.
Both cameras are very satisfying to use, and lenses from Leica and Carl Zeiss are really terrific. You can't go wrong with either a Summicron, Summilux or Planar.
I would recommend that you handle a Bessa, a Zeiss Ikon and a Leica and see which one suits you best. You might find that the Bessa best fits your hands and shooting style. On the other hand, it might be the Leica. Or the Zeiss Ikon.