Comparing between similar types is usually fairly straightforward, I'll use daggers (1d4 to small) and short swords (1d6 to small) as an example.
Orcish equipment is usually weaker than its counterparts, doing 1 fewer max damage to small monsters. (1d3 for dagger, 1d5 for short sword.)
Elvish equipment is the opposite, dealing more damage to small monsters (1d5, 1d8.) Elvish equipment is also non-metal, except for the mithril coat. The weapons are wood.
Dwarvish equipment is similar to elvish, but metal. In general their armours helps one additional point, while their weapons range from slightly stronger (spear) to slightly weaker (short sword). They do not have a special dagger, but their shortsword deals 1d7 points to small monsters.
Silver weapons are identical to standard versions, but deal an extra 1d20 to certain creatures. (werewolves, shades, demons)
Comparing across types is more complicated, there isn't a great rule of thumb, and it is highly dependent on the weapon skills you have. Usually the weapon skills worth having or using, if available, are Long Sword(includes Katana), Dagger, Saber (Grayswandir or silver saber with twoweapon), and Mace (Scepter of Might). There are times when you will be using other skills, of course, but given two weapons that seem equal, one that trains/uses these skills will usually be superior to one that does not.
I think you might have gotten some misinformation. Yellow dragon scale mail provides acid resistance, not stoning resistance. In fact, in vanilla Nethack it's not possible to achieve intrinsic or extrinsic stoning resistance at all, aside from polymorphing into a stoning-resistant monster. The confusion might be due to the fact that acidic monsters are useful as a way to prevent stoning (by eating their corpses).
Your idea of wielding a cockatrice corpse as a weapon is not an uncommon strategy, but you need to be wearing gloves at all times and you must be extremely careful, because there are lots of ways that something can go wrong. You may want to wear an amulet of life-saving just to be safe.
Best Answer
According to the wiki, the Scale Mail has a base AC of 4, and the Banded Mail has a base AC of 6. But with the +2 enchantment on the Scale Mail, they both have an AC bonus of 6. Then, the only real difference between them is the weight. As you mentioned, the Scale Mail is substantially lighter, so it is the better choice.
The one benefit you might get from keeping the Banded Mail instead is that it has a higher potential AC bonus, after enchanting. All armor can be safely enchanted to +5, which means that a fully enchanted Banded Mail will have a higher bonus than a fully enchanted Scale Mail. However, this is relatively early game armor, so I would not use armor enchantment scrolls on these when you could save them for a Dwarvish Mithril-coat or a Dragon Scale Mail that you will hopefully be using later in the game.