Fiber paper has several advantages to RC paper, but it does take a little more work to get the most out of it. The look and feel of a well processed fiber print just can't be matched by RC, and the fiber print will last much longer. The range of finishes and the textures of the many fiber papers out there generally make RC papers look sort of cheap in comparison.
As for differences in processing, as I said, fiber paper takes a little more work. First, it typically needs more time in the developer and fixing baths, not to mention the wash. Secondly, it tends to curl, and needs pressing to flatten prints once dry. RC paper generally needs 60-90 seconds in the developer, and about the same in the fix. Fiber paper, on the other hand, should get two to three minutes in the developer for complete development, and it needs four to six minutes in the fixer to clear completely. Many printers will fix fiber papers in two fix baths, splitting the time between them. The second fix bath will be cleaner, and this helps ensure proper fixing. Finally, fiber paper will need more time in the wash (typically three times as long as RC needs to wash)- especially if you aren't using a permawash. Fiber paper generally takes toning more readily than RC, too, so if you are toning, watch for faster and more radical color shift than you get with RC papers.
More information is available on the web and in print, and I recommend you do some research- but good fiber prints are really wonderful, and the extra effort is well worth the results. Have fun, and let us know how it goes!