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: 
Let's start with the difference between progressive and non-progressive JPEG files.
Non-progressive JPG files ar not by definition smallers than progressive JPEG files. A rule of thumb found by Stoyan Stefanov is that JPEG files smaller than 10K are best compressed non-progressive JPEG, but that bigger JPEG files become smaller when stored as progressive JPEG.[source](http://www.bookofspeed.com/chapter5.html) see the chapter progressive JPEG.

So if you just want the smallest download non-progressive is not always the best choice.

This 2012 article goes into more detail [Progressive jpegs a new best practice](http://calendar.perfplanet.com/2012/progressive-jpegs-a-new-best-practice/)

Tip if you want even smaller JPEG files use [mozjpeg](https://github.com/mozilla/mozjpeg)

But now to anwser your question.
You wanted to know if anyone has actually done any research on user preferences.
Well actually someone did.

You can read an article on the research by Tammy Everts here: [Progressive image rendering: Good or evil?](http://www.webperformancetoday.com/2014/09/17/progressive-image-rendering-good-evil/) It contains a link to where you can obtain the full report.

Spoiler: users seem to prefer baseline JPEG files over progressive.
+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).