They begin their article with a 4-page list of all animal experiments known to them with viruses of these 4 kinds. Brief scrutiny of the list suggests that adenoviruses have drawn the most attention. The first attempts at viral transplant of DNA in animals used Herpes viruses. That immune reaction limits the length of time the implanted gene continues to be repressed. In the worst cases, it may only be a few days.
Herpes viruses have the same problem as adenoviruses.
In the case of adenoviruses, considerable work has gone far towards removing these problems, but more remains needed for clinical application. Neither Herpes nor adenoviruses actually implant their genes into the genome of the target cells, while AAV viruses and AIDs virus can do so. These two latter also cause much less immune reaction. All have sufficient capacity for use in nervous systems. To use a virus to insert a gene into a cell, genetic scientists have used two different methods, each one really the poles between a range of possibilities.