E. coli and s. epidermidis were chosen to represent gram-negative and gram-positive bacteria, respectively. for a given antibiotic, is there a difference in susceptibility between the gram-positive and gram-negative bacteria?

Gram-positive and Gram-negative are different in their resistance to antibiotics. It is because of their different structure of cell wall. Gram-positive bacteria have a thick peptidoglycan cell wall and dyes purple in the Gram test (for categorization of bacteria). Gram-negative bacteria have thin peptidoglycan layer and do not turn purple. Gram-positive bacteria are easier to kill because their thick peptidoglycan layer absorbs antibiotics.