These are benadryl's side effects:
SIDE EFFECTS: Diphenhydramine can commonly cause sedation, tiredness, sleepiness, dizziness, disturbed coordination, drying and thickening of oral and other respiratory secretions, and stomach distress. Diphenhydramine may also cause low blood pressure, palpitations, increased heart rate, confusion, nervousness, irritability, blurred vision, double vision, tremor, loss or appetite, or nausea. Diphenhydramine should be used with caution (if at all) in persons with narrow-angle glaucoma, prostatic hypertrophy (enlarged prostate gland), hyperthyroidism, cardiovascular disease, hypertension, and asthma. END from the MedicineNet site
Prozac is a serotonin uptake inhibitor, used to treat anxiety, depression, and sometimes panic disorders.
Its side effects can include: dry mouth, constipation, urinary retention, sedation, and weight gain (and more; there's much more to read about Prozac, needless to say).
So some of the side effects may overlap. Also, Benadryl can exaggerate the possible sedation effects of the benzodiazepine anti-anxiety drugs (Valium, Ativan, Klonopin, Xanax), the narcotic-type pain medications (like Percocet, Vicodin, Dilaudid, Codeine, Darvon), and the tricyclic class of antidepressants (like Elavil, Tofranil, Norpramin).
The basic active drugs in the two (Prozac, or fluoxetinen, and Benadryl, or diphenhydramine) are not similar at all, to the best of my knowledge.
One is an antihistamine/anti-motion-sickness agent and one is a selective serotonin re-uptake inhibitor (SSRI).
P.S. This is all based strictly on what I've read. No chemistry education here. :>D