It all has the same effect on the brain.
While most opiates generally have the same effects, different opiates have different levels of those effects. Ask anyone who has taken fentanyl and then needed to stop taking it whether it has the same effects as hydrocodone.
Different opiates are metabolized in different ways, and produce different quantities of various metabolites. Some even have different routes based on the user's health. Oxycodone, for example, has a higher k-opioid receptor response in diabetics, while in non-diabetics the antinociceptive effects are achieved through u-opioid receptors.
Additionally, the "brain effects" wear off for most long-term users when used to treat pain.