Generally, automatics will have less felt recoil due to some of the energy being directed to work the action. As such, the recoil profile will be different, though the overall final value will be the same. You'd be violating the laws of physics if some of the energy just disappeared.
That's basically the right idea. Autoloaders tend to spread some of the total
momentum that is transferred to the shooter (i.e. impulse or recoil) over time so that the peak
force that one feels is a bit lower, which in turn is perceived by many as less "felt recoil."
As for energy conservation, although energy doesn't simply disappear, not absolutely all of the energy of a cartridge that does work, as opposed to being wasted as heat or escaping gas, is used to propel the bullet. A small amount--just a few foot-pounds, I would estimate--from each cartridge is used to cycle the action, and some portion of that energy will eventually be used to ignite the primer of the next cartridge that is fired. You already knew this, but my point here is that this is a very small amount of energy in comparison to the bullet's kinetic energy. If, hypothetically, it were enough to make a noticeable difference in the felt recoil on its own, then it would take a substantial amount of energy away from the bullet, making autoloaders somewhat inefficient firearms. Some people actually seem to believe this, but they would be wrong--only a few foot-pounds are involved, in the low single digits for most handguns.
In a revolver, the energy to cycle the action and ignite the next primer comes from the shooter instead of the cartridge (although the same is true when the shooter initially racks the slide of an autoloader, it doesn't count because each cartridge must still provide some energy for the next cycle). However, those who believe that revolvers are therefore more efficient with the energy of cartridges are forgetting about the cylinder gap, which loses surprisingly little energy but probably a bit more than cycling the actions of autoloaders, I would guess.