Hi Bethany -- thanks for posting your question. Story Maps are responsively designed so that the on-screen elements, like the side panel, will resize based on different screen resolutions, browser window sizes, and aspect ratios. Also, below a certain size the layout will switch over to something that is more mobile friendly. Currently, however, the text doesn't resize (other than when the story switches over to the mobile view).
Could you please share the resolutions of the two monitors you are working with and perhaps even screenshots of the text and content on each monitor? It'd be helpful to see the differences you are seeing so we can consider addressing this in a future release.
You may be able to design around this by choosing an overall smaller text size that looks better at more resolutions. Also, developers can download the code for our Story Map apps here on Github and customize it with HTML, CSS, or JavaScript to add behaviors that aren't currently included. You can read more about how to do that here.
Owen Evans
Lead Product Engineer | StoryMaps