Here's an article that explains this well, http://www.surfbirds.com/ID Articles/dowitchers1005/dowitchers.html
Here's the specific quote, "Tail feather pattern is one plumage feature that is believed not to change significantly with age. It is often cited as a very reliable field mark (Wilds, 1990; Jaramillo et al., 1991; Jaramillo and Henshaw, 1995): on Short-billed, the white (or buff in alternate plumage) bars on the tail feathers are reported to be as wide or slightly wider than the black bars (Fig. 8) whereas on Long-billed, the black bars are wider than the white (or buff in alternate plumage) bars, sometimes even twice as wide "(Fig. 3).
Edit: I just realized your photos are from California, which would mean you'd have likely have the pacific subspecies of SBDO, so there is possible overlap between this subspecie of SBDO and LBDO when it comes to this feature according to article
2'nd edit: MerMaeve, if you zoom in close enough you can make out the tail pattern