Which of the following sentences is more suitable?
- He delivered me to Peshawar in a BMW.
- He carried me to Peshawar in a BMW.
Should I use delivered or carried?
It might be delivered, but that sounds like you were a package.
The car carried you not the driver.
A better alternative would be
He drove me to Peshawar in a BMW.
You deliver things- a parcel, some goods, a meal. You do not deliver people.
When you carry comething, you move it bodily- in your arms or on your back.
You could consider eiher drive or take. both would imply that he is driving the car.
"He drove me..." is neutral.
"He delivered me..." implies that your presence at Peshawar had been demanded. "The boss sent for me. I was delivered to Peshawar in a BMW." Or there's a (possibly humorous) implication that the passenger(s) were considered as goods. "We called the girls' school for some dancing partners. Several were delivered in a BMW."
The sentence is about taking someone to some place in a car, so delivered is more appropriate.
Here is a related definition of deliver given by Macmillan:
deliver
1b. to take someone to a place where they will be guarded or taken care of
deliver someone to: He was safely delivered to his hotel.
The other choice, carry, can be used for taking someone (or something) somewhere, too, but if the trip happens in a vehicle, it's used when the vehicle does the action (i.e., the vehicle is the subject of the sentence), not the driver. For example,
carry
1d. if a vehicle carries someone or something somewhere, it takes them there
An airplane carrying 120 passengers has crashed in India.
I think the best phrase is "He brought me to Peshawar." That leaves any question of vehicle type or reason for going completely out of the phrasing.
"Brought" is still the best choice for modern English usage. "Delivered" and "carried" both have a strong connotation of a non-human object; "brought" can be used with human and non-human objects.
According to the current text of the question, it is impossible to answer as there is not enough context. By what means of transport did you get to Peshawar?
'Carried' implies 'carrying by hand', which is normally unlikely. 'Delivered' is normally used for a package, but might be suitable here. 'He drove me to Peshawar in a BMW' is probably what you want.