For indoor applications, oil insulated transformers typically will be required to be installed in a fire-rated vault. For outdoor applications, there is a fire hazard to nearby structures and other transformers. Oil transformers are generally considered more reliable and are most common for outdoor installations.
Dry type transformers are typically less expensive and do not require a vault when installed indoors. The insulation is susceptible to moisture absorption, which reduces reliability particularly for outdoor applications or where the transformer is not energized at all times. Dry transformers are most common for indoor installations.
A variation of the dry type is the encapsulated coil type which reduces the moisture problems, but is significantly more expensive.
A fourth option is non-flammable or 'less'-flammable liquid insulation. This has the reliability advantages of oil insulation, with minimal fire hazard. It can be used indoors without a vault in many cases. It is generally the most expensive of the four types.