If your MOBI books have DRM, then FBReader won't work.
For DRM-free MOBI files, FBReader is essentially as good as MobiPocket's own Reader at rendering the e-book on the screen. Its primary disadvantages are: that page turns are slow (the next version may fix this) and images bigger than the screen won't rescale. Its advantages are: choose any font you want, choose any line spacing and margins you want, customize lots of other stuff for how you like to read e-books.
If you have a Linux (or Mac) Desktop, then FBReader will work and MobiPocket Reader won't.
FBReader reads many other formats without conversion. Since most MOBI files have small images, when there is a choice I use the LIT version instead. This can be converted to a MOBI file (with large JPEG images) on a Windows desktop, but FBReader will read the LIT directly after ConvertLIT explodes it (which can be done in-line on the iLiad).