T3 is for shorthaul, such as palm spring and vegas

T4 is for 'all the rest"/longhaul

between T3 and T4 is Tom Bradley the int'l terminal. walkiing time is aboout 10 minutes

the AA shuttle leaves roughly every 10 minutes. it is faster to go from T3 to T4 (you just have to past Tom Bradly) following the anticlockwise flow of traffic, and it takes longer to go from T4 to T3.

but 20 minute is enough to move between terminals. it you have tighter time window, you can choose to walk (pass Tom Bradly, i.e.)