In our modern world, Prozac is used to treat major depressive disorder, anxiety, bulimia, and obsessive-compulsive disorder. Basically, Prozac is an anti-depressant.
On the other hand, SOMA in the Brave New World is an opiate or opioid. Opiates are naturally extracted from the opium poppy. Opioids, on the other hand, are either manufactured chemically (synthetic) or modified from natural opiates (semi-synthetic). Today, the term "opioids" refer to either synthetic, natural, or semi-synthetic opiates.
Either way, opioids or opiates are narcotic in nature: when taken, they generate a sense of well-being, reducing tension, anxiety, or aggression. Opioids also trigger euphoria, stupor, apathy, and in extreme cases, coma and death. The narcotic nature of opioids like SOMA differ from the anti-depressive nature of a modern drug like Prozac.
Prozac works by affecting the level of certain neurotransmitters in the brain. For example, it is said that the neurotransmitters serotonin, dopamine, and norepinephrine are associated with depression. A drug such as Prozac is an SSRI (or selective serotonin reuptake inhibitors): it increases the level of serotonin in the brain, as lower levels of serotonin are said to contribute to depression.
So, Prozac differs from SOMA in that it is not meant to induce euphoria or dull the senses. In Brave New World, SOMA is said to be "Christianity without tears." It is also described as "Euphoric, narcotic, pleasantly hallucinant." In Brave New World, SOMA so dulls the senses that the person taking it is unable to recognize the reality of his existence. However, Prozac and SOMA are similar in that they are very effective in reducing symptoms of anxiety and/or depression.