It’s probably because of the spices. That’s hard for non pro to find very good quality cardamon and cinnamon. Other possibility, they let their big pot “at the corner of the fire” where milk can’t boil, there tea and spices can give their full flavour during the hours they infuse.
For that point you can “cheat” at home, the 1st time the milk (with all the rest then) is boiling take the pan out of the fire (the time to recite a mantra ^^), put the pan on the fire again until the milk retry to escape and out. do it 5 to 7 times and you should have a tastier chaï, closer to restaurant .
