The one marked "Dixon & Sons Patent" is a shotgun powder-flask.
Of course, we should always keep in mind that an internet seller's statements on time-dating and value tend to vary widely, and be inaccurate. For example, the following internet seller:
A Near Mint Large English Powder Flask by, DIXON & SONS, PATENT
says your particular version of Dixon & Sons Patent powder-flask is from the late-1700s to early 1800s... but Dixon & SonS (plural) did not exist until 1835, which is after the "late-1700s/early-1800s." The company used that name from 1835 to 1920. Check the company's Chronology at:
James Dixon & Sons - Sheffield
The company stopped manufacturing shooting accessories in 1915.
To see another match-up for your Dixon & Sons shotgun powder-flask, priced at 200 British Pounds (about $300), go here and scroll down to the sixth flask:
ORIGINAL POWDER FLASKS AND SHOTBAGS
In doing a lot of internet research on your powder-flasks, I've noticed that almost no sellers give a specific time-period for the Dixon & Sons flasks, because the company used the same marking on powder-flasks from 1835 to 1915.
Because valuable antique powder-flasks are known to have been reproduced, and markings can be faked, you might consider paying for this powder-flask ID service:
Powder Flask Identification