Ok, know this might be mis-understood, but ... one has to be careful of mixing terminology of 'teaching' using the same terms as moodle mods/blocks/activities. From your description am understanding that a 'lesson' isn't really the lesson mod in Moodle, it's a course. You mention 'book' ... is that the 'book' add-on (you may have had that installed on the old version)?
If the backup contains 'book' (as in Moodle addon book), then the site must have the 'book' add-on installed for the backups to be able to restore 'book' activities. No book add-on, no book activity is restored ... Moodle just skips it - ie, missing.
Also, when it comes to the actual file size of the backups, while that does require an increase in upload parameter, the size isn't really an indicator of just how much processing is needed to restore a course. Quiz, for example, is a heavy/resource hungry activity in Moodle that when one is restoring, requires more of the server. That means some more php tweaks might be needed ... amount of memory a script can consume, the max time a script can run, etc..
When restores fail, check the following:
apache error log
moodledata/temp/backup/ directory - for clues.
'spirit of sharing', Ken