I have a problem with database imports, so far I've tested this behaviour on 3 machines, one is our hosting provider.

This ipb database is an upgrade from ipb2.3 with fixed special characters (sed tool), so it is in pure utf-8 format.
The thing is that if I use different export / import tools, database size differs on import - mostly bf_message_posts and ibf_posts tables size vary, since they are biggest.

This various sizes were observed when (I alway use mysql console tool for db import):
- if I export database via phpmyadmin and reimport it via mysql tool, size goes over 500MiB
- if I export database via mysqldump and reimport it via mysql tool, size stays the same (about 360MiB)

I've migrated this dump to my hosting provider and reimported it via bigDump script (http://www.ozerov.de/bigdump) - size goes over 500MiB - those two previously mentioned tables grow on import by 70%.

Why are these size differences observed with different import/export methods, since the content seems to be the same?

maybe its character conversion?

Indeed it is. Also server global charset comes into play.
In the end I was unable to port DB to UTF-8.