If price is not an issue, then I recommend the iLiad over the BeBook for fiction reading providing you use FBReader. This works very well on the iLiad, and reads DRM-free MOBI as well as many other formats. I don't read many PDFs, but the iLiad's PDF capability is head and shoulders above that of any 6" EInk screen device.
The Java MOBI reader that comes with the iLiad reads DRMed MOBIs, but it otherwise provides barely acceptable reading experience. It does provide dictionary support though. I have not used a BeBook, but its MOBI reader is based on the same Java reader as the iLiad. The BeBook does not currently have dictionary support. The BeBook has a separate reader for FB2 etcetera which may be better, and it can even run FBReader.
I am very interested in OpenInkpot
on the BeBook. It isn't quite all there yet, but an Open Source software stack that includes FBReader and a PDF reader could be very good if work is put into filling in the rough edges. In the worst case, OpenInkPot does not fill your needs and you are left with the original firmware which is probably good enough. OpenInkPot may get ported to other EInk devices, but the numeric keypad of the BeBook provides more options for the user interface.