In terms of differences, eukaryotic cells are much larger and more complex than prokaryotic cells. On average, a typical eukaryotic cell is about 1,000 X larger in volume than a typical prokaryotic cell.
This means both drugs (amoxicillin and penicillin) can treat a wide variety of infections. However, unlike amoxicillin and penicillin, the routinely prescribed drug, metronidazole, has a more selective action towards anaerobic bacteria. These bacteria are the ones causing the signs and symptoms of bacterial vaginosis.
Penicillin antibiotics kill bacteria by disrupting the production of the bacterial cell wall, causing the microbes to burst. According to the University of Maryland Medical Center, amoxicillin was once one of the most commonly used penicillin antibiotics against urinary tract infections.