Sawfish (and others) have some good points, but some details need clarification. Probably more then you want to know, but...
1) Bullet expansion with today's technology is based on design fabrication and build geometry in addition to material properties. Cases in point. The black tipped TAC-TX bullet by barnes for the 300 blackout is all copper and designed to (and tested to) function (expand to 2x original diameter or 0.6 inches) down to ~1300 or 1400 fps giving it a ~300+ yard range with the rifle
Other bullets are designed to expand at the typical velocity they will be used at. Hornady makes 2 version of the 30 cal flex tip 140 gn rifle bullet. One for the 30-30 (lower expansion velocity) and one for a 30 cal marlin express (higher expansion velocity which is a bit faster.
When you are working up a load, call the manufacturer and find out what the minimum expansion velocity is and make sure your bullet is traveling at least that fast at the ranges you want to shoot.
2) because they are longer, use the reloading information supplied by the manufacture. Most of the new bullets have grooves cut in the bearing surface to reduce the bearing surface and chamber pressure to more "normal" ranges for given velocities and loads.
3) One of the unique features of copper bullets is that they typically retain all or nearly all their weight (don't shed a large fraction of their weight in small lead particles in the tissue). I don't shoot typical pistol and haven't seen much info on retained weight in pistol bullets other then that posted here (most examples shown here tend to retain most or all their weight, i assume this is because of lower initial energy), but rifle bullets can lose a huge fraction of their lead core in the animal depending on the bullet design (see the download report here for some examples
http://www.dnr.state.mn.us/hunting/lead/index.html) One of the results of all this is that most copper bullets are expected to pass through since they don't shed their energy in explosive destruction of the bullets core on impact.
I have not hunted or shot the Barnes bullet for the 357 or any other handgun, but expect it would stay intact and turn into a 0.7" mass of metal passing entirely through the animal if used as directed. If you can, use a chronograph to determine velocity and then calculate max functional range and stay within for best bullet performance.
as always, placement, placement, placement, much like location in real estate.