Yes the BAT may be somewhat warmer than the Freya. Many would prefer that. I have heard BAT amplification and enjoyed the experience.
The Freya is very good at it's price point, however as aforementioned the BAT is built to a higher standard.
BAT is (has) going through management/owner changes and my only concern would be service for a used unit. Not to declare service a problem, however I would look into that if interested in a used unit.