Usually when the Church honors two or more saints together on the same feast day, it is because they were martyred together (or in the same persecution). There are a few exceptions: Cyril and Methodius (whose feast day is Valentine's day!) were brothers, joined not only by the bonds of blood, but by their shared mission as evangelizers into Eastern Europe. And today's saints, Basil and Gregory? Even though Basil's own brother is also a saint, it is Basil's lifelong friend, not his brother, who shares today's feast day.
Basil "the Great" and Gregory "the Theologian" were not two peas in a pod. They were very different in personality, but both were fabulously gifted scholars and writers. We had to read Basil's works on monastic life when we were novices. I don't think I understood very much! But much later, I read Basil's "On the Holy Spirit," and still keep in on my shelf of "favorite books." As for his friend, Gregory, my chief memories are from my days in Rome: there was a bishop who always celebrated a 7:00 a.m. Mass at the altar above St. Gregory Nazianzen's relics. (Later, Pope John Paul II restored those relics to the Eastern Orthodox Church, for whom this Gregory is one of the three most important theologians in history.)
I'm trying to think of other saints who share a feast day, but not a martyrdom. Any ideas?