Dragonscale is thick. It's Euro 4-1 woven inside another sheet of Euro 4-1, and not really much else. It looks very nice, and the sheer weight will provide protection, but if I had my choice of armor I'd go for some 6-1 or 8-2 (Kingsmail, or "double 4-1") instead.
Chainmail is made to protect against slashes. Namely swords and sometimes axes, though many axes are just small-contact blunt weapons so take that as you will. It's hard to cut through chainmail because you end up gliding your blade along many rings, and the armor will deform slightly and "cup around" the blade to provide a larger contact area and thus a smaller PSI-force. However, chainmail is NOT made to protect against piercing weapons. When a speartip hits chainmail, it hits one or two rings, and at any respectable force it will simply pop the rings open and slice right through them. Once a few rings are destroyed like that, the piece loses its structure and the spear doesn't have to shove through as many because the sheet will give way more easily. This is even worse for bullets, being such a small projectile, they only need to get through one right.
So imagine that you've got one ring set in a vice, and a sharpshooter with a handgun shoots that ring. You can imagine it's not going to do anything to really stop the bullet. Chainmail is terrible protection from bullets.
Scalemail is made by taking leaf-shaped pieces of metal sheet and layering them one over another. Many times you get the whole thing four sheets thick, as the overlap densely, so you'd not only have to penetrate one scale, but you'd need to get through 3-4 of them, depending on how large they are and how your body is flexing to shift the weave a little. Some type of solid titanium scales would probably be pretty effective at stopping bullets, but titanium is extremely expensive stuff, and ultimately I'm going to fall back on my old excuse. "I'm just getting into this, but others have spent their whole lives researching this. I'm going to trust their experience." My logic here would be that ceramics are much cheaper, not to mention incredibly lighter and easier to replace. Not to mention the function. Metal armor serves to be brutally thick. If it's heavy, then things just can't get through it. Ceramics, however, rely on more reactions, they're intended to break and to diffuse pressure as they fracture. It's a very active defense, compared to "lol imma brick wall."