In general, Shotokan will have longer, lower stances, while Goju will have higher, more upright stances.
Shotokan stylists have a reputation for focusing on Kihon (the basics). Expect to do the same kick or punch over and over, working on the details.
The amount of sparring done in a school is pretty much up to the teacher, based on the way he was taught, and his particular inclinations. Some Shotokan schools may spar more than others. Likewise with Goju. Karate stylists, in general, do not emphasize tournament competition to the same degree that Tae Kwon Do does. There are pros and cons to competing and not competing.
There is no overlap between the katas of the two styles, according to their kata lists on black belt wiki: