This will be a short post based on my experience in dealing with students and players who are choosing a new saxophone.
Most of the time, whenever a musician asks me to try a saxophone, once he goes into the tryout room, I can predict more than 99% of the time exactly what he's going to do once he gets in there. He/she begins playing scales at rapid speed. Up and down, down and up, mixing them up, but always playing them fast. Now while I know that sound and tone is subjective, so many so-called players will hand me back a perfectly good or great horn and say, "it's no good". Frankly, they don't know most of the time what they are looking for.
However, most of the time, there is one thing they do not do in order to properly evaluate a saxophone, or any other brass and woodwind instrument for that matter. While playing fast scales may give you a good idea how well the keys respond to your playing, that's not the whole thing. I've said it before, I'll say it again. It's the SOUND! If you really want to know the core sound of your horn, which I consider the most important thing, then play a slow blues or a ballad, and really dig into it with each note. Stretch the notes out, make them sing!
The other thing players do when playing fast scales is also to play at the same volume, usually loud. That doesn't really tell you anything about the horn either. Use dynamics in your playing. Go from soft to loud, loud to soft, and so on. Go slowly from the lowest to highest notes, then back down, and really listen to the response from your horn. See if the horn has a balanced sound from top to bottom, or if something changes as you make the transitions. Sometimes the problem may not be the horn, just a simple thing like a change in reed or mouthpiece, although don't go overboard with it. Don't start going crazy endlessly trying mouthpieces and reeds or else you'll lose sight of the actual playing.
If the horns sounds good or great, it is! The keys can be tweaked by a competent or expert technician, and a mouthpiece or reed will also help improve the sound, but the horn, and the player themselves will have this quality, or not!