You didn’t mention one obvious (to me, at least) reason why both “with animal” and “doing something interesting” result in more contacts/conversations: the animal/activity are conversation starters. Or, in sales terms, “hooks”.
. . .
Note that “with animal” and “doing something interesting” tend to be just about equal in all your stats.
So, for a sure fire hit, one can assume that “Doing something interesting with animal” would be one’s best(iality) option?