does unlocking get rid of the mobile operator software etc?

A2 unlock using Aerix client will preserve all operator branding and software. Also, your data and settings should be preserved

DB2020 unlock will remove branding and operator software (well it actually depends on what firmware you download. If you have a T-Mobile branded phone for example, and found the correct T-Mobile firmware for your region, then I guess it would still be branded. Most people just get the generic firmware, which does mean that branding and operator software is removed). Data and settings are NOT preserved, so you will need to back this up (ideally to a memory card, which you can then remove).