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: 
+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).
The main difference is that when the picture (jpeg file) is export as "progressive" is going to load the full size image with reduced quality, while if it's export as "optimize" is going to load section by section from top to bottom.