"Open With" now appears in the window that opens after I tap on the three bars on the right, and if I select Open With, the file opens in my default app. I'm assuming that's the result of a Dropbox update that my Samsung tablet installed automatically. However, the "Just Once/Always" window doesn't appear, and Dropbox still doesn't honor default app the way it used to.
In the past, checking "Always" set the default for a file type--say, pdf to illustrate. After doing that, the next time, all that was necessary was to click on or tap the pdf file in Dropbox. Dropbox opened the pdf in the default app. There was no need to use the "three bar/Open With" process.
Now, the "three bar/Open With" process is needed each time. The file will open in my default app--a two-step process, instead of a one-step process. Simply tapping the file opens it in the Dropbox viewer.
Note that, in Dropbox settings>Manage defaults, the app that I want as the default is shown. Open With launches that app. Tapping the file itself does not.