I can see why Si is a tandem function of Ne. It is supposed to compare current sensations with past sensations and in a detailed manner, and Ne is supposed to compare one thing to another, connect different things based on their similar patterns. (This is not to say that Se is not detailed, but probably not in the same way.)
Similarities. Si and Ni are both left-brained functions, and they both cooperate with a primary or secondary function to produce a "left-brained person", if that even makes sense. And since they are both left brained, they are both very categorical people.
Differences. Maybe understanding Ni is supposed to allow you to understand Si. Ni creates and analyzes things based on non-apparent, future possibilities. Si renders and analyzes things based on a thing's conformity with established things. They are both concerned with the way things should be, but with different emphases. My ISFJ brother appreciates MBTI more than he appreciates Socionics, because, according to him, MBTI has been around longer, and thus more tested, whereas I am equally drawn to Socionics as to MBTI, since Socionics is just a different spin on MBTI.
I am inclined to believe that both Si and Ni users converge on their conclusions eventually. The TypeLogic website indicates, for example, that ISFJs and INFJs reach the same conclusions through variant processes. This is not to say, of course, that ISTJs and INFJs reach the same conclusions.