The Neo has no indexing, but it does have support for a full folder structure which permits you to arrange your books however you like. It also has a "Most recently read" page, which gives rapid access to the books you've most recently opened. It has search (within a book - not between books) and supports dictionary lookup with any dictionary in the popular "Stardict" format.
You can't have multiple books open at once, but you can switch between books with two button presses or stylus taps - press "Back" to return to the "Most recently read" screen, then tap the book you want to open.
The nice thing about the Neo is that, although it has a Wacom touch screen, the user interface is fully operable with the buttons, too, and can be used equally well left or righ-handed, since the navigation controls are in the centre. It can comfortably be held one-handed. The only thing you have to use the stylus for is things like text highlighting.
I've leave it to someone else to comment on how the DR800 compares, since I have no personal experience of that.
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