It's super important that we have a choice. Just like legislation that forces new construction to use obscure sockets for CFL's, bullet regulation hinders innovation and progress. I am personally, absolutely against lead and use only lead-free primers. I have no exposed lead anywhere on my firearms, ammo or reloading bench. But I am even more against government regulation of bullets. It's counterproductive.
For meat game, I wouldn't shoot anything else -- Barnes TSX, TTSX, Hornady GMX, Nosler E-tip. For shot I'd use steel, bismuth or tungsten. I'd even use bismuth for muzzleloaders unless I had the twist rate to shoot saboted copper. I don't see the point of contaminating meat with lead. But I even choose Barnes XPB or TAC-XP for civil purposes, entirely because of the terminal performance -- given the cartridges of my choice.
Others have pointed out some of the characteristics of solid copper. They're not necessarily disadvantages, but they do require forethought and accommodation. Copper projectiles can be engineered to open at a goal velocity, but to give them the toughness to avoid shedding petals, TTSX tend to perform best at higher velocity. Still, many TTSX have minimum velocities for expansion of as little as 1500 fps and perform very well at 1800fps or more. The handgun TAC-XP and XPB perform very well at 1100 fps or more and may not be the best choice for self-defense ammo in the most popular cartridges, but can work superbly in .357 Magnum (where I use them) and in the big bore hunting magnums. .357 Magnum is a good example of a cartridge that is optimized for solid copper bullets. Because copper is not as dense as lead or tungsten, a bullet with the same sectional density is going to be longer. In a rifle, that could call for a higher twist rate (but the VLD, ELD trend is going that way anyway). In a handgun or an AR-length intermediate cartridge, we need powder capacity. 9x19mm minimizes powder capacity for grip size. It simply isn't optimized for copper bullets. .357, on the other hand, provides plenty of space for the long bullet and enough powder to drive velocity well over the requirements.
With rifle rounds, copper bullets change some of the old standards for bullet weight and sectional density. For example, a 140 gr. bullet would have been considered "standard" for a .264" caliber with lead. With copper, a 120 gr. bullet will probably serve for the same purposes. Copper's toughness compared to lead means that lighter bullets will penetrate better than heavier lead bullets that shed their weight in the target, drastically reducing their sectional density as they go. A hundred years ago, people would use a 30 caliber 170 or 180gr bullet to shoot deer. Today, a 100 gr. copper TTSX in a smaller caliber will perform at least as well. But you can see from the 220 gr. pictured in the post above, fast and lightweight isn't the only way copper can be made to work, though subsonics are probably going to work like handgun bullets without remote wounding effects from hydrostatic shock. But if velocity is the key to shock wounding, then lightweight copper that will hold together at high velocities is going to have the advantage.
I am in a state that does not regulate lead or bullets. But the only thing I shoot lead for is the low cost. I shoot copper plated bullets (handgun) and hollow-point (rifle) bullets so there is no exposed lead on the bullet and no lead in the bore or vaporized off the base (FMJ). I also shoot only lead-free primers. This keeps lead off my guns, off my reloading bench, out of my tumbling media, out of the air I breathe, and off my hands. I would shoot solid copper or sintered metal bullets exclusively if they were less costly and in the case of sintered, were ballistically closer to solid copper. As it is, the XPB's I shoot in handguns are 10 times more expensive than the copper-plated bullets. The .357" 158 gr. RMR plated hollowpoints are excellent substitutes for the 140 gr. Barnes XPB as they're nearly the same length, and due to the difference in start-pressure, both take about the same powder charges. At practical handgun ranges, the POI is close enough and again I can shoot 10-times more bullets for the same expense. For .357 Magnum, there is comparable but no better terminal performance than the Barnes XPB in any bullet.