I don't know, the Hand don't really get any play outside of the Legend of the Rangers pilot and JMS seems to be moot on the subject, which of course, is really annoying since any fanon has to be carefully considered to not contradict canon that's already been established. From what I gathered, the conflict against the Hand was never intended to go into a full blown invasion of the Milky Way and become an all-out war like the Shadow or even Drakh Wars. I believe that the plan was that there would be a major battle going down that would essentially reseal the Hand back into exile, similar to that of Thirdspace.
Interestingly enough, the original premise of the Legend of the Rangers would've dealt with the aftermath of the Shadow War and explained their legacy and how it affected the universe (whereas Crusade was focusing more on how the Shadows infiltrated and manipulated high levels of Earth Force). So, if that's the premise, what does the Hand have to do with this?
Well..... here's my theory. If indeed the Hand are as powerful as they claimed to be, and it is true that they were sealed away over a million years ago (or billion, I can't remember), then it seems that the force of light that stopped them in this little corner of the galaxy would've been the First Ones.
Now, remember, Minister Kafka said that the Hand were even more powerful than the Shadows, which if true, would mean the other First Ones would not be a match on a 1-v-1 scenario. The only hope that the First Ones have, are to pull together and fight as One. Now think about it.... which race has always emphasized teamwork and unity? The Vorlons. And because their is strength through teamwork, this becomes the cornerstone philosophy that the Vorlons would wish to past down to the younger races.
However, in this case, the Vorlon method of alliance and unity is not enough. While definitely curbing the Hand advance, it's not enough to push back. The Hand with their war-like ruthlessness continues to push through in certain sectors until they finally are met by a race that's just as bloodthirsty and power-mad as they are. These of course are the Shadows. And because the Shadows revel in chaos, they evolved much faster than the other First Ones and offer the Hand an enemy that can actually go one on one and NOT lose. However, the Shadows do not have nearly enough man-power to completely engage the Hand, so they decide to pull their forces with the other First Ones, and together, they drive out the Hand and seal them into an unknown dimension.
Fastfoward a bit to where the younger races are finally coming around, the Vorlons and Shadows take it upon themselves to prepare the 'children' to be strong against what lies ahead. The Shadows want the younger ones to evolve quickly, so that they will have the confidence to be able to thwart anyone who attempts to harm them, and the Vorlons want them all working together so that no single power will be able to dominate them.
Both sides understood and respected these positions and thus came to a compromise and took several races under their wing. The Shadows would teach the Drakh, Zener, Taratimude, Wurt, Ikarrans, etc, and the Vorlons would work with the Minbari, Narn, Centauri, and Humans, etc.
However, when it became clear that certain races excelled differently and began to determine their own paths, this caused a conundrum. (The Centauri were already proving to be more well versed in Shadow philosophy with the constant fighting against the Xon, and the Taratimude near the end, opted for Order and created the Technomages). Eventually, wars broke out between younger races, and then the parents (Vorlons and Shadows) began to step in, but at this point were so engaged in resolving their ideological differences, began to only exasserbate the process to the point where as to paraphrase Delenn in "Into the Fire", "you've been fighting each other for so long, you've forgotten why".
So, yeah, to make a long story short. This story idea would be the explanation of what originally started the ideological conflict between the Vorlons and the Shadows.