How to identify when to move all or part of the data from Sybase ASE to Sybase IQ?
Tough call. Look at it from a transactional RDBMS versus reporting-style OLAP perspective, at a high level. The IQ methodology is column-store, versus a traditional row-store for ASE. Column-stores are very fast when running aggregated queries over them, but that depends on how your reports are run, right?

I think you almost nailed it with this:


  Ok, we have a lot of data archived and need better timings retrieving
  it, we should go to IQ!


So, do your analysis on volume of data you'll be querying all round, that is fairly static or slowly changing. If that's going to be queried a lot, look into IQ.

Don't be scared of a hybrid solution either. I have several SQL Server customers that have massive warehouses running with columnstore indexes, right in the same cabinet as their highly transactional RDBMS.