Ballad - Definition, Meaning & Synonyms | Vocabulary.com
A Very Strange Question

Ballads can be played on any saxophone (well maybe not sapronino lol).  The question you need to answer is what horn do you prefer to hear ballads play on.  
When I think of sound quality, it is more dependent on a players oral cavity and embouchure, mouthpiece choice, and reed.  The actual horn generally has less influence on sound than those aforementioned factors.  
The bad news is that you can't just go buy a horn and get the sound you want.  You have to make the sound you want through practice.