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 is mostly effective against this type of bacteria, since it kills bacteria by disrupting the peptidoglycan cross-linking process. Gram negative bacteria, including E. Coli , have thin polysaccharide walls overlaid by thin layers of lipopolysaccharides.