I assume that archiving means moving data from one database to another correct?

It depends what your boss want, if he wants a small compact database then you have to archive, if data older than 5 years is not needed anymore then archive

If you dont mind have a huge database then just partition, if you need the last 10 years data then partition

Archiving is not that simple though, depends on your data model it can be a nightmare archiving data since you have to archive from child to parent, grand parent, gran grand parent and so on. Work out all those dependencies probably takes you months.

Partition isnt too bad, a fast way to reduce a huge table into small segments but then again there are limitation such as global indexes needed to be rebuilt if partition structure is changed, such as merging or splitting partitions. In OLTP systems mostly we use global indexes so it quite a headache if you have a 1000 million partitioned tables and you need to add a new partition which cause a rebuild of all global indexes in the table.

Regarding versions, if you wanna move to 10g I suspect you need to upgrade your Developer Suite as well, I am not that sure if 6i is certified against 10g (except Oracle E-Business Suite of course). Upgrading Developer is tough if your 6i applications are server-client based because moving to 10g Developer Suite means you need Oracle Application Server and migration to three tier architecture. Lots of things to consider. 10g database is very powerful though, ASH is specially helpful.

It's all about depends....