Most cabs use 3/4". One reason is because it's far more available than 5/8" material. 1/2" material (the next step down that is wildly available) is probably too thin. Also there are a lot more options for T molding in 3/4" than 5/8".
If I had easy access to 5/8" material, I'd use it. But I'll probably be using 3/4" sanded (one side) birch plywood for my cab since it's fairly close to the same cost as 3/4" MDF locally but quite a bit lighter.