There are some characteristics not mentioned. there are copper jackets, as compared to copper/tin/zinc. the all copper jackets tend to scrub off material in the bore so tend to foul the bore more than the alloys, but they tend to bend rather than split on impact, so they generally have better terminal performance- yielding classic mushroom shapes. the old Barnes .049" jackets were good examples of this, except that the core wasn't bonded, so at some point the core would separate from the jacket- in most situations the separation occurred after the bullet had delivered a killing wound so wasn't an issue- but was sufficient to lead Bill Steigers to develop his Bitterroot Bonded Core bullets, which are the model that Jack Carter copied for his Trophy Bonded, and then by other makers.
For monometal the same holds true with regard to bending rather than splitting, however the pressure is affected. A lead core allows some distortion due to the bullets contact with rifling which doesn't happen with an all copper/alloy bullet. the initial Barnes X bullets had a reputation for higher pressures due to the non-compressability. This issue was addressed even back with the Nosler Partition where the partition portion of the bullet was turned down to bore diameter. the current solution is to have bands cut into the bearing portion of the bullet so that there is space for the metal to push into when the rifling displaces it.
There has been a great deal of research into reducing the detrimental aspects of the monometal bullets in internal, external and terminal ballistics and has been noted above by several, this research has paid off- which appears to be a good thing, considering the political environment regarding the banning the use of lead in any form and for any purpose.