I have a trove of civil war letters. They were all letters home written by a Union soldier from New England. They detail his travels, his work, and his life. Included are dozens of pencil drawings of people and places he saw. There are probably between 50-100 letters.
I have been in contact with a state museum , and a large library from his hometown. How do I make a determination as to who will benefit best from this material?
There's always more that can be said, but I have a past post on what to do with historic archival materials that may be useful.
I'm assuming that both places were receptive when you brought up the donation? You should consider telling each of them that you're in talks with the other and see if either says, "Oh, the other one is a better home for these," or "You know, we don't really have the space for this, so if they want them that would be great." That being said, it's highly possible that they'd both be fine repositories and the choice is just down to which is easier for you to deliver the letters to. It's really not a situation where you need to feel a lot of moral weight on your shoulders.
Since they are documents and not artifacts, I'd think that a library (if truly large enough) would be more likely to have the infrastructure to archive them in a way that made them publicly accessible. Have you asked either institution what plans they might have or develop for public access or display? When you ask this question, be aware that there are sometimes grant resources available for help with projects like these, depending on the scope.