Both choices are correct in the proper context, but they are not interchangeable. “Neither” and “none” serve different purposes.
Both refer to only one person, place, or thing in a group, and thus they each require a singular verb, but “neither” is for one of two items, and “none” is for one of three or more items.
TWO PEOPLE, PLACES, OR THINGS
The phrase “neither of them” is correct if you are talking about two people, places, or things.
(The verb should be singular, because you are selecting only one of the two persons, places, or things.)
THREE OR MORE PEOPLE, PLACES, OR THINGS
The phrase “none of them” is correct to describe three or more people, places, or things.
(The verb should be singular, because you are selecting only one of the group of three or more.)
Both refer to only one person, place, or thing in a group, and thus they each require a singular verb, but “neither” is for one of two items, and “none” is for one of three or more items.
TWO PEOPLE, PLACES, OR THINGS
The phrase “neither of them” is correct if you are talking about two people, places, or things.
(The verb should be singular, because you are selecting only one of the two persons, places, or things.)
- “The store was selling both pink and yellow roses, but neither color would look good in my garden.”
- “I have two sons, but neither of them lives near me these days.”
THREE OR MORE PEOPLE, PLACES, OR THINGS
The phrase “none of them” is correct to describe three or more people, places, or things.
(The verb should be singular, because you are selecting only one of the group of three or more.)
- “Many universities are located in my state, but none of them is in my town.”
- “All the plants in your garden are quite healthy, but none of them is native to this area.”
