The two affect the viewing area in the eyepiece, however, in different ways.

Extension tubes magnify the subject area but knock the DOF down to darn near nothing. Great for macro isolation.

Teleconverters magnify the subject by doubling focal length. DOF is reduced in regards to increased focal length. However you may experience poorer image quality and a slight light fall off.

As to which might be suggested would completely depend upon what you wish to do.