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Hi,
A short and easy explanation about the difference between the 1.3.x and 2.0.x serie is that XOOPS 2.0.x uses the smarty system. Smarty is a system to keep layout seperated from coding, on this way, we are able to have a more powerfull system so users can control more without the knowledge of php. You might wanne use search for more info about all of this.
To upgrade from XOOPS 1.3.x to XOOPS 2.0.x is very simple. First, remove ALL files, then upload the XOOPS 2.0.x files, run /install/, after a couple of tests (when checking database) it will discover the XOOPS 1.3.x tables and will automaticly start the upgrading progress.
Hope this was helpfull.