All the special things about your weapons and armor will remain the same. So if you have a piece of armor that allows you to carry more pulse rifle ammo for example, that will carry over into the Crucible. All that is done in the Crucible is that number stats are ignored. You'll notice that each weapon has bars, with no numbers, that determine things such as how stable it is, how much "impact" it has (damage) and rate of fire, among a few others. These are the stats that the game uses to equalize the weapons in multiplayer, so the gun will feel pretty much the same in multiplayer.
They're probably either already doing this or won't for reasons of principle, because I can't imagine it being that hard, but could we get some numbers to go with those bars, for those of us who have display issues or eyesight issues or memory issues or spatial interpretation issues and can't compare bars that well? If they aren't as finely gradated as they seem, maybe descriptive terms, like high, low, moderate, very low, exceptionally high, moderately low, etc. You could have those even if the bars are very precise, and have them apply to a range, for getting a good general assessment quickly. Maybe just lines dividing the bars into sections.