Question: I know that progressive jpegs download in multiple passes, and optimized are smaller (and thus faster to finish downloading), but does anyone have any hard data or best practices on *which type users actually prefer*?

Answer: 
Here's an alternative perspective on it. Not an absolute rule, but a thing to keep in mind.

**It depends on what the image is for. Content, or decoration?**

If it's a background or other design element, use progressive, so the page looks okay-ish as soon as possible. If it's an element that moves stuff around, it needs to be there ASAP so people don't mis-press a button due to layout shifting. (been there a couple of times on mobile.)

If it's content the user is going to download, or consciously pay attention to, use regular JPGs. This communicates to the user that it's not yet finished, that they have to wait a bit. This stops them from saving an unfinished download, and they won't experience the site as bad quality but the server/connection.
+1 to DA01

If OP is referring to reduced file size as "optimized" then here are some standard practices when saving as JPEG.

1. Don't embed color profiles. Browsers these days have better ICC
profile support.
2. Export image as sRGB
3. Set metadata to none
4. [Set quality at 65%](http://laurashoe.com/2011/10/18/jpeg-quality-compression-lightroom/). More about quality settings can be found [here](http://regex.info/blog/lightroom-goodies/export-quality-tester).
5. Ensure the file size and dimensions are in scope of your requirement. i.e. don't export a 2000x3000px image for a mobile website.

More about Optimizing images [Guide by Google](https://developers.google.com/web/fundamentals/performance/optimizing-content-efficiency/image-optimization?hl=en).