This one is the older of the two, built, according to a Bud Phillips article in a 2105 issue of the Bristol Herald Courier, in 1910-12. The card was printed in 1950.
This card was also printed in 1950. The article mentioned above states that this hotel was built in the 1920s.
Coincidentally, both hotels went away in the 70s. Hotel Bristol, abandoned by then, burned down. The Shelby was demolished.
A couple of notes: The sign “Hotel Bristol” has been enhanced by a retoucher, as has the sign for the Shelby. All the windows have shades. All are exactly at exactly the same level. Retouching, again, I’m sure.