S104XXX: S&W used the "S" prefix for 12 different models built on the "N" or large revolver frame, but only one of them was chambered in .38 Special: the .38/44 Outdoorsman Model of 1950, which became the Model 23 in 1957 when model numbering began. Yours was made in 1954. Nice. Very nice.
S160XXX: 1955 .45 Target Model, the precursor to the Model 25. The one you have dates from 1956-57. Also very nice. I have one about 9 years younger than yours, by which time they had started using the "N" prefix. It's one of my favorite range guns - I load .45 Auto Rim for it (I'm one of the oddballs who hates using moon clips).
Value depends a lot on condition, and the gun (guns? - I can't really tell if it's one gun or two) in the photos appear to be in great shape, particularly for its (their?) age. With the run-up in revolver prices lately, I think you're looking at several hundred, perhaps close to a grand for each.
BTW, you correctly identified the "S" prefix numbers as the serial numbers. The other numbers stamped in the yoke cutout, and sometimes elsewhere, are so-called "assembly numbers" used to keep track of fitted parts during the manufacturing process.