A photo that I stole from someone else on this site a while back. Bullet on the left is a 130 gr copper bullet, right is a 180 gr conventional bullet.
A stout cup and core bullet will still lose about 20-25% of its weight and end up at around 130-140 gr. The copper bullets will retain near 100% of their weight. The end result is about the same.
Everything I've read about copper says 180 gr bullets are best used at magnum speeds. A 30-06 may not shoot them fast enough to open up except at pretty close range and on tough animals.
I run 180 grain barnes TTSX in a 350 remington mag for whitetails.
180's in a 350 mag are a light, fast bullet, just what you are looking for in copper. A 180 in a 30-06 is a heavy, slow bullet. Everything I've seen and read indicates that you get best results with at least 3000 fps at the muzzle. I've loaded some 130's @ 3050 in my 308 and 150's just over 3000 for my 30-06. I think those are the optimum weights for those calibers, but the 180's should kill a deer. It just wouldn't be my first choice.
Here is a good article talking talking about copper bullets. Some good photos showing how important impact velocity is. Below about 2400 fps at impact doesn't offer much expansion.
http://www.thediyhunter.com/big-gam...bullets-tsx-ttsx-243-wssm-270-wsm-rifles