Although with a bit of patience, creativity and maybe with the aid of some good flashes you can safely use your Diana with any kind of film, the CN800 offers easily the most flexibility.
Negative film is usually a very tolerant medium; if you have a scanner, and are able to use it properly, and if you have a pinch of creativity (even with a small tripod you can work wonders), you will be able to make pictures with virtually any kind of film. However, having a flexible negative at hand can be a huge help — when you do not have time to find a fix spot for your camera, for example, or when you want to have overexposed highlights on your picture. The stong, crisp contrast of low-sensitivity film can also be distracting when you try to make pictures in places (like a forest), when patches of light are scattered on larger patches of shadow. You want details in the highlights, without making the shadows pitch black.
Gloomy winter days, with the Sun behind thick layers of cloud does not offer much light — if you are, like me, a Diana lover, you will find that even on the brightest areas, all you pictures are get underexposed even with the “Cloudy” (f11) setting; in narrow streets, when houses shade out even more light, your pictures will get dark.
The Lomography CN 800 film does offer a solution for all of your problems.
Besides being very affordable, it has beautiful colors and a wonderfully soft grain. You can work with it virtually under every kind of light conditions outdoors but the brightest sunlight — as said above, negative film is a very tolerant medium and is much more tolerant towards over exposures then underexposures, and it does not have a strong contrast — your pictures are, of course, will be less dramatic, but sometimes this is precisely what you want.. Usually (having a light meter does help) you can decide where you want to put the exposure: you can show the details in the shadows, or you can create good highlights outlining the darker areas. Overexposed areas will still have some detail, which you can still strengthen during scanning if you wish.
If you are using the Diana with a flash (it is an excellent companion to the Lomography Ringflash), you will have much more ambient light on your photos — since the film is more sensitive, you will pick up more of these.