The correct wire for both 50A and 60A circuits is 6 AWG Cu or 4 AWG Al. That is because you are required to pull from the 60 degree C column of NEC 310.15(B)16, which says 55A, and you are allowed to "round up" to the next available breaker size.
At large sizes such as 4 AWG, there is no earthly reason to waste money on copper wire, provided that breaker, socket and any splices be rated for aluminum wire. Certainly if you are going a long distance, and needing a size bump to reduce voltage drop, aluminum is the right stuff.
There has been a problem in the past with people (including electricians) installing 40A circuits for Tesla chargers, using 8 AWG Cu wire, and finding they must then upgrade to 6Cu or 4Al. That happens because the Tesla charger is labeled for 40A, and they're forgetting NEC 210.20(a) which requires 125% of rating for continuous loads, and 625.40 which affirms it for EV chargers. Don't install 8 AWG.