Markov Chains & Long-Run Behavior · Hard problem

Two rival models predict how customers switch between Coffee Shop A and Shop B each month. Model 1: $A$ keeps a customer with probability $0.7$ (otherwise switches to $B$); $B$ keeps with probability $0.6$. Model 2: $A$ keeps with probability $0.65$; $B$ keeps with probability $0.55$. Under which model does Shop A have the higher long-run market share, and what is the positive difference between the two models' steady-state shares for $A$? Express your answer as a common fraction.