590nm offers the most color of the IR filters, with vivid colors in the vegetation and sky. The color can be manipulated in many creative ways in post processing. For B&W, it is not quite as good as the higher filters since simply desaturating the images does not produce good B&W contrast. However, if you convert to B&W with a tool that allows you to adjust the tones of the individual colors, the results can be essentially just as good as the higher filters. Another benefit of 590nm is that you can use all the other higher IR filters on the lens (assuming the camera has liveview mode), and in that way it is the most versatile of the IR conversions. Exposure length with the 590nm filter is similar to a normal camera.
720nm is a good all-around filter, though I would say it is slightly better for B&W than color. Its color IR effects are subtler than 590nm, but some people prefer its look. The sky and some other objects will have some color, while vegetation is colorless. For B&W, simply desaturating the images produces excellent B&W contrast. Also, higher IR filters like 830nm can be used on lens (assuming the camera has liveview mode). Exposure length with the 720nm filter is similar to a normal camera.
830nm is a completely monochrome filter that offers the highest B&W contrast, but it comes at the cost of exposure length that is a couple stops longer than with the other IR filters. Since 720nm offers very nearly just as much B&W contrast with shorter exposure times, I usually recommend it over 830nm, even for people only interested in B&W IR. However, some people simply want as much B&W contrast as they can get regardless of exposure time, and for that 830nm is the best choice.
The full spectrum conversion leaves the sensor unfiltered and thus provides the ability to use any of the IR filters on the front of the lens. It also allows the use of other specialized filters such as for astrophotography or ultraviolet photography, and it is therefore the most versatile conversion of all. However, it is really only suitable for cameras with liveview mode, which allows the camera to see through the IR filters when they are put on the lens. Thus, mirrorless cameras, compact cameras, and DSLRs with liveview mode all work fine as full spectrum cameras. On the other hand, older DSLRs without liveview mode are unsuitable for full spectrum conversion because they become inoperable when an IR filter is placed on the lens. I should note that people sometimes think that a full spectrum camera can be used for normal photography by putting a UV/IR-cut filter on the lens. However, this is only partly true because UV/IR-cut filters do not work correctly in front of wide angle lenses (they cause a color-shifting vignette), and for that reason I do not recommend that a full spectrum camera can be used as a full replacement for a normal camera.