I use OpenInkPot on my EZ Reader Basic (Hanlin V3, same as BeBook). You can get a idea of how well it will display your ebooks by using the Windows or Linux Desktop versions of FBReader. The OpenInkPot version is fully up to date, and includes many of the customization options of the Desktop version. Note that new users of FBReader are often put off by the default setup, you really need to customize the font, font size, margins, line spacing, etcetera to get an idea of what it will do. With OpenInkPot you also get the option of long pressing the file selection key to bring up CoolReader instead of FBReader (when both support the ebook format). See
File Navigation: Hanlin V3 vs OpenInkPot for how the file interface differs (not by much overall). This also discusses ebook formats to some extent.
Note that MOBI and ePub are not rendered the same in FBReader as in a "native" Reader like MobiPocket or ADE. FBReader started out supporting no CSS at all, instead using a global set of user provided layout preferences. Recent versions (including the OpenInkPot version) support a subset of the CSS used by ePub (and MOBI). Purists don't like the partial support, and I preferred the original simple screen layout but can live with the current approach. You should try a few ePubs in the Desktop FBReader to see what you think.