comfort softs are probably the closest to a mid range real tyre.
Comfort hards do not give you more control, the opposite infact.
Better tyres = a faster slide but the balance is just the same,
A fast car with good tyres will be similar to a slow car with **** tyres in almost every way except speed.
Real life competition drifting requires a LOT of grip to allow the speed (you'd be left for dead in a tandum on shat tyres)
However a budget drifter may go out of their way to lower grip in order to slide a slower vehicle.
Horses for courses there's no "drift tyre" comfort hards are easy and last for ages, I'm sure last time I tried mediums they didn't last half as long.