In the States, you will hear both. However, the "eee" version is most common, while the "eye" version can sound aristocratic, pretentious or condescending. If someone is, in fact, from an upper-class family, the "eye" version is acceptable and even expected.
There are some areas of the country where the "eye" version is MOST common, and does not sound pretentious, specifically in the Northeast (New England states).