The Young Chang and Bergmann are pretty much the same. They both have Renner actions which are great. I believe they are both made by the same people. The Young Chang model is specicifally built for weather conditions in Australia.
The Yamaha model is also built for Australian conditions. Yamaha has it's own action. Yamaha sets the piano key travel on it's uprights to match the travel on it's grands. There is something to be said for that. Of course once a piano technician gets a hold of that it could change, depending on the technician.
You didn't say what model the Horner is. Check the soundboard and see if it is imprinted in English or German. If English it was made in Denmark and is a good home piano (if in good condition now).
You might find your nearest piano technician that will be doing the tuning and service on your piano and see what he or she is trained in. As I eluded above a Yamaha piano serviced by a technician not aware of Yamahas requirements won't be the same afterwards.
Which one would I choose? I wouldn't choose any of them. I would find a beat up, broken, cracked piano from a local college that's been abused (preferably a Steinway)pay $100 and then I would rebuild it. (But then I know how, have the tools, and can).
For you?! I would narow it down to the Yamaha or the other two. The Yamaha has a fantastic adjustment period service plan that comes with every piano.
The other two come with a 12 year guarantee I believe. (your used Horner won't). The Bergman is less expensive and it is made by Young Chang. The Bergman has the same action as the Young Chang. I would purchase the less expensive one made by the same people.
Yamaha will have a little bit brighter sound.
Young Chang and Bergman may be a little more mellow or darker sound.
