After reading the various reviews, and peoples' praise, I decided to give Droplr a try.
I want to love it. But I don't.

Notes for context:
a: I'm not interested in browser extensions, so my experience is based on using the desktop (menubar) apps themselves, and my references to "the browser" are actually to using my account's browser page.

b: I'm using MacOS Mojave. So if you use Windows, your experience may vary.

Droplr cons:

1. CloudApp lets me drag multiple files to the menubar, and they upload as separate items. (Droplr zips them and leaves them there as a zip, which is useless when I want to visually scan for individual files, both in menubar app and on webpage.)

2. When I do a screen-record with CloudApp (gif mode), the gif is viewable on other machines fine. With Droplr, other machines just get a blank white screen and no video ever plays. With both the direct downloaded file and with a link to the browser page. Not useful if you can't view the recording!
This makes me really feel like I can't trust Droplr.

3. Rename. In CloudApp I can rename a file from the menubar app and it actually renames the file. Droplr requires me to use the browser, and even then only changes the display-name of the file, but the file itself is still misnamed. Downloading or dragging the still-incorrectly-named file to any app, like email etc, still leaves me wondering "which file was this again?". Renaming should be simple.

4. Annotating. CloudApp's icon bar for choosing annotations lets me quickly choose an annotation type with a single click. Droplr makes me click and hold a dropdown to choose the kind of shape or pen etc. It's just that little bit slower and less friendly to use.
Annotation options: CloudApp lets me quickly select alternate line thicknesses and text sizes (Okay, to be fair, I finally found the font-size chooser in Droplr after trying a hidden click-and-hold action).
CloudApp also offers cropping and "spotlight" to fade out a background to draw attention to just a certain part of the image. I've used these more often than I ever expected to!

5. CloudApp lets me push the snapshot into my clipboard for immediate use for pasting into any app. Droplr only creates links.

6. CloudApp lets me control password/security/expiration access from its menubar and annotator. Droplr requires using the web interface.

7. Preferences. CloudApp gives way more control over its menubar app than Droplr does.

8. CloudApp's "record desktop audio" has allowed me to get rid of another app I used to use for sending audio-only messages to my team.

Droplr pro's:
- Annotator's default color palette - I like Droplr's default "green" shade better. Yup. I told you I want to love Droplr!
Features that look intriguing, and made me want to try out Droplr, but haven't really explored because of the essentials being weak, include the "other media types" (Markdown notes, Code Snippets, other URLs shortened).