That is great advice from CA357.
My very uneducated and general observations:
The first one appears to be a flintlock pistol that was converted to percussion.
You probably also noticed the ramrod is missing. It looks vaguely military to me, rather than say a civilian dueling pistol. I found one similar at this link:
Look for the one from the Napoleonic period.
The second smaller pistol looks like a percussion cap pocket pistol , sometimes also referred to as a "derringer". It rather reminds me of the gun J. Wilkes Booth used to kill Lincoln. Go to this link and you'll see what I mean:
Certainly the first gun seems to be in far worse shape than the second, but an expert could tell you if its of any value. Good luck.