I’d guess it to be a 1830’s-40’s, the “golden age” of gilt buttons, many of which had geometric patterns like this one. But seeing the backmark, or at least part of it, would help confirm this.
That backmark was used from 1834-1848. They made both military and civilian (like yours) buttons. The picture below shows other examples of the geometric designs popular in that era, as well as some of the floral designs.
The small button is from about the same time, considered a “Jacksonian cousin” as described at the link below. I believe it would have had a rim around it as do the examples shown there. The rims can be broken off, as we have seen here on some dug examples. http://www.thebuttonmonger.com/content/November 2011.pdf