Bernafon and Oticon belong to the same Holding (William Demant). They have their own research institutes (Bernafon in Bern, Switzerland).
They share the accessories (streamer, programming interface), but the hearing aids are different. Someone here told me that they use the same chip platform, but I have no different source to confirm this.
The software (I don´t only mean the programming software, but the software on the aids themselves) is completely different. Bernafon uses a “channelfree” approach, and is the only manufacturer to do so.
I have the bernafon Juna 9 aids and am very happy with them. But I haven´t tried oticon.
From what I´ve learned on the internet, Bernafon aids are quite different from other aids - you love them or you hate them.
In case you try bernafon aids, be sure to try nal-nl2 as a fitting formula, I didn´t like bernafit (their own formula) at all!
PS In case you want to do further research, it might help to spell the name right