Common by itself can mean either
prevalent[Oxford, sense 1] or
shared[Oxford, sense 2].
Occurring, found, or done often; prevalent:
- salt and pepper are the two most common seasonings
Shared by, coming from, or done by two or more people, groups, or things:
- the two republics' common border
However, in expressions like
interests in common or
interests common to them, the meaning is restricted to
shared. To avoid ambiguity, it is a good practice to phrase your sentences like this if you wish to imply the second meaning.
So, the second sentence is talking about shared interests. The first is likely too, but not necessarily. It could be interpreted to mean common, boring, pedestrian interests.