So are you going to get an electrician to do this or are you going to do it yourself? If you're getting an electrician to do it, they could run 6/3 MC cable or some other 75C wiring method; that has an ampacity of 65A and you could protect it with a 60A breaker. That would let you set a small 60A subpanel in the garage to feed multiple receptacles.
If you are doing it yourself, you probably want to stick with NM cable with its 60C ampacity. Cost-wise you'd be best off using 6/2 NM (the EVSE doesn't use a neutral, running it is a waste of copper), a 6-50 plug and receptacle (or hardwire the EVSE), and then maybe one 12/3 NM for a MWBC with two receptacles on it, one on each leg. Although maybe the MWBC would be too much complexity, you could just run one 12/2 NM for a single 20 amp circuit with a 5-15 duplex receptacle on it.
As to the OP, if you're going to the trouble to run the 6/2 (or 6/3) NM that distance, the marginal labor to also run the 12/2 (or 12/3) NM would not be great. Probably a good idea. As to code issues, if you use a single PVC chase for both cables (I suggest upsizing to 1-1/4" PVC for ease of installation), you'll have to derate the cables for bundling. But the way the numbers work out, that has no impact, see below for details.
Derating: NM cable is limited to the 60C ampacity for conductors, which for #6 Cu is 55A, and for #12 Cu is 20A. [And #12 is also limited for most circuits by the small conductor rule to a 20A breaker.] However, NM actually has 90C conductors inside of it, and for derating purposes you're allowed to take advantage of that. The 90C ampacity for #6 Cu is 75A, and for #12 Cu is 30A. The derating factor for 4-6 current carrying conductors is 80%, so the derated ampacities are 60A for the #6 Cu and 24A for the #12 Cu. These are both still greater than the 60C ampacities, so there is no net reduction in ampacity for the bundling.