Folks have gone on for pages on the pros and cons of lead vs. copper, both from an environmental and a practical hunting standpoint, and this little piece from the NY regulations pamphlet manages to lays out the key issues of the debate in a couple of low-key pages.  Everyone, on both sides of the issue, should take notice.
Yes, lead can kill scavenging birds, and that's something that every sportsman who enjoys his time outdoors should consider when choosing ammo.  But, at the same time, for low-velocity applications, lead does the job quite well, and isn't likely to cause much harm to scavengers because it doesn't fragment through the meat.  And low-velocity situations are just the places where monometal copper bullets are most likely to fail.
I became a convert to copper for big game a couple of years ago, when a 115 grain Barnes TSX gave me superlative accuracy (1" @ 200 yards) in a .257 Weatherby Accumark.  I've since found that the TSX consistently provides better accuracy than quality lead hunting bullets in other rifles (120 gr TSX in .280 Rem, 140 gr. in 7mm Rem, 225 gr. in .340 Weatherby).  And the downrange performance is just fine, with ten animals ranging in size from steenbuck to kudu and gemsbok (and including multiple pronghorn and mule deer on this side of the Atlantic) all falling to a single shot at ranges between 60 out to about 225 yards.  Penetration was great (the .257 will shoot through a pronghorn lengthwise) and destruction of vital tissue substantial (everything forward of the diaphragm often looked as if it was poured out of a can of Campbell's Chunky soup), yet meat damage wasn't at all bad, despite the rifles' high velocities.  Shots were taken at all angles from directly ahead into the chest of the animal to a sharp quartering-away shot, and each time, the bullet performed perfectly.  And as a bonus, I never bit down on a hunk of meat only to find me molars crunching into a piece of bullet jacket or similar fragment, as happened frequently when a traditional jacketed lead bullet brought the animal down.
At the same time, when I go into the thick woods, seeking whitetails with my .44 Ruger carbine, the rifle is loaded with plain old 300 grain Hornadys.  As much as I like Barnes bullets, I don't trust them to open up and perform reliably at .44 mag. velocities, and concerns over losing a wounded deer (or perhaps a black bear) outweigh my worries about possible lead poisoning of scavenging birds--and with the big bullet leaving the rifle at less than 1400 fps, I'm not to worried about it breaking up into a bunch of easy-to-swallow pieces anyway.
So I'd argue that the NYS DEC article (which is probably shorter than this response) sets the right tone:  Neither the "lead bullets must be abolished" harrangues on one side, nor the "lead is harmless" claims from the other get the whole picture right.  A tool must be appropriate to its purpose, and in hunting bullets, both copper and lead have their place.