If you are working within the recommended pressures for your gun (check the manual) then reloaded bullets should work just as well as new bullets. Exceeding recommended pressures will wear the gun out faster and may cause varying degrees of damage, especially if the gun is not designed to handle it.
One caveat to that is the use of unjacketed bullets. You should not shoot unjacketed bullets in guns that have polygonal rifled barrels, such as Glocks. They can lead up quickly, boosting the pressure in the gun and shortening the lifespan of the weapon.
High velocity bullets must be either partially or fully jacketed. An unjacketed bullet fired at a high velocity could become deformed and leave behind a detrimental amount of lead in the rifling grooves of the firearm. Lead deposits can lead to poor accuracy and may damage the feeding mechanism.
Guns that feature a gas-operated mechanism, such as the Desert Eagle, should not be loaded with unjacketed lead bullets. The lead particles sheared off when the bullets are fired could clog the gas release tap, which can malfunction.