Yes, the advanced epubs are just the zipped source repo, which is epub 3.2, including any "advanced" CSS selectors and so on. "Advanced" here just means that the epubs are written with a modern web rendering engine in mind, while most ereading platforms in the wild are still at an IE6 level of CSS/HTML rendering support.

The "compatible" epub is the same epub, but with various compatibility enhancements automatically added for different ereading platforms.

Currently only web browsers can render the advanced epubs at 100% fidelity. iBooks might be the only non-browser ereading platform that does a pretty good job with the advanced epubs, as I believe it uses modern Webkit as its renderer. For any other ereader, use the compatible epubs. (Or kepubs for Kobo.)

Would you have any Android reading app recommendation for advanced epubs? There are android ereaders, those should surely be able to handle any epub given the right app, right?

Lithium seems to be fairly good in terms of rendering our advanced epubs, but it's not perfect; note especially that it doesn't invert black-and-white SVGs correctly so unless you set it to a dark page theme, they'll be "invisible". There are also some other rendering quirks for things like very big tables used for play formatting.

Poor renderers are a perennial problem in the epub world and there seems to be little interest in improving the situation. Just use the compatible epubs - for reading purposes they're almost equivalent except in some rare edge cases. Or, you can use our 'read online in browser' option to read ebooks directly in your web browser, which will serve you the source of our advanced epubs. But of course reading in a browser is less than ideal.