Gloss is much harder not to damage, obviously. Otherwise I would say it depends on the subject matter. Technically, gloss is better for reproduction purposes whether that be an internegative or a paper negative. The pebbled finish of matte can/does cause just a slight blurring compared to a clean gloss print.
With gloss, you can achieve the sharpest image - obviously depending on your negative. With mat, it depends on the particular finish of the particular paper you use.
The modernists (Adams, Weston, etc.) advocated gloss paper in their turn against the salon pictorialists, so gloss was considered more serious for a while. I personally use Azo, and you can read a great deal about it at michaleandpaula.com.
Today, though, people seem to use what they like. It depends on your photographs and what you want to convey, and how you want to do it. Get some paper, experiment, and go with what you like. I really don't think anyone other than you can tell you what to print on and talking won't take the place of experiment.
As Fred Picker (not a god) constantly said, "Try It."
As other have said, with FB it does not really matter, but in this case my preference goes to air dried glossy (it actually looks semi-glossy). The real difference between glossy and matte shows out in RC. I personally feel that Ilford Multigrade IV RC glossy has a plastic-like look that does not match my taste. Pearl is something of a compromise. Matte has a very nice finish, but the tone are a bit dull. I'm about to test matte RC with selenium toning.
If you havent realized this yet from reading other excellent and practical posts: it depends on your personal vision of the print and what you expect to do with it. If fine detail is required then RC glossy may be best. Or if mood and quiet, softness is desired maybe matte or semi-matte. I find that most of my prints look best to me on RC pearl or glossy FB with no Ferro-typing.
Up to now I have had no facilities in place to properly dry and flatten FB prints so have concentrated on using RC products. Whilst I love the look of RC glossy in terms of "snap" the high level of gloss can be a pain to view because of specular reflections. Pearl never moved me much but thats just a personal view. I have just purchased some Kentmere Art Classic and Kentmere Document Art. Both a matte surfaces so I will be curious to see how I like them, having mainly stuck to glossy paper for most of my time as a photographer
While I agree with everything that has been said (esp. re: Fred Picker) I can't stress enough that you have to find your best paper, and don't be surprised if you have a different favorite paper for each negative. Make the print that is closest to your personal vision, then print it again on a different paper, different brand, different base, different surface. You may surprise yourself that the image you thought you were printing turns out to place a poor second to a new paper. Look in the galleries and see that out of 12 images by one artist there may be two, three, or more papers represented. Not every negative prints best on one paper.
I keep coming back over and over to my favorite, but I'm never so smug as to restrict a negative to one paper. There are always 4 or more other papers in the drawer.
Each respondent can tell you what he or she likes best, but only you can answer the question.