Using WoWWiki and WoWHead, I compiled a table of all epics that drop in Naxxramas-10. And it appears that there are no "common" and "rare" drops, every item on the loot table of a particular boss has an equal chance of dropping. Clear Naxxramas-10 five times, and statistically speaking you have one of everything. In reality of course Murphy's Law applies, and you get several times the epic nobody wants, and the most wanted thing doesn't drop at all. :) But the loot table gives us an idea for what raid composition Naxxramas is designed, or which classes have the best chances to gear up there.
I didn't go into details of classes and talent trees, for that you'll have to look at WoW-Loot. I just sorted the loot into cloth, leather, mail, plate, and other, with other including all sorts of weapons, off-hand items, jewelry, and trinkets. I subdivided plate and other into categories of caster, melee dps, and tank. And I subdivided leather and mail into caster or melee. I didn't count tokens.
The result was that there are 16 cloth items, 16 leather items, 15 mail items, 24 plate items, and 53 other. The cloth is obviously all for casters. The leather and mail is split half and half for casters and melee/ranged dps. The plate has 9 caster, 8 dps, and 7 tank pieces. And in the other category there are 26 caster, 21 melee/ranged dps, and 6 tank pieces.
The count confirmed my suspicion that there is 50% more plate dropping in Naxxramas than other armor. Which is curious, because there are three plate-wearing classes and three cloth-wearing classes, so there should be equal amounts of cloth and plate. The easiest class to equip in Naxxramas-10 would be a holy paladin, who has 9 pieces of plate nobody else can roll on, plus the largest selection of other items. The hardest classes to equip would be a protection warrior or paladin, a long-standing tradition of Blizzard. Cloth wearers have the biggest competition for armor pieces, but benefit from the largest selection of other items. For mail and leather wearers there are a lot of items that are useable only for few classes and builds, which makes loot distribution there depend strongly on what classes and builds are actually in the raid.
Only about 10% of the epics in Naxxramas-10 are specifically for tanks, a bit more if you count items useable for feral druid tanks. Over half of the epics are for casters, that is healers and spell dps. So for loot purposes a "perfect" raid would only have one tank, 3 healers, 2 spell dps, and 4 melee dps. Teach your death knight to off-tank in dps plate gear, and you're golden. :)