The reasons for rearming varied widely and there seems to have been no overall policy to standardize on a certain rifle like the Springfield. However, various units did sometimes try to standardize ammunition and I've seen examples where rifles were moved around to have certain brigades, etc. all use, say, .58 cal. ammo.

Other times units were anxious to get rid of old or inferior arms and replace them with better ones. Often this depended on the "clout" of the commander. Sometimes the unit's home state would get involved and furnish them with better weapons, and there are even examples of civilian "subscriptions" to buy better arms.

There are also examples of units doing "battlefield upgrades" when they felt that captured arms were better than what they had. This was surprisingly frequent in Union outfits.

So I guess the answer is that you'd just have to dig down in the records and correspondence and see if you find what the reasons were, as they varied greatly.