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Basically, the mod version should be the last thing you update, for the simple reason of there might be db changes in the newer mod vs the older mod version. When I upgraded from a 1.3.x site to the newer 2.0.6 version, it took me a while to get all of the existing mods up to speed. Most of them worked, but there were a few that don't work, yet that is. Basically what I suggest doing is import all of your tables into your new db. If you have updated versions of modules, you might look at the table structure of those modules to see if there are any changes. I ran into this when I updated a module. If there are changes to the db structure, then you need to make sure that the tables in your old db match the db structure of the newer more updated versions of the tables.
I know this sounds confusing, but it creates less headache and problems and potential data loss.
1.) Compare DB structures of the modules first. If they are the same you shouldn't have any problems. If they are different, you need to make sure that the older tables, the ones that you will be importing, match as far as the actual table structure is concerned.
2.) Export each table locally then import them into their respective tables in your new db.
CROSS YOUR FINGERS!! Migrating data is a pain, and personally I haven't found an easy way to get around it.
If you need any more help, don't hessitate to ask.
Hope this helps