Instruments make a difference, and...
First, yes, instruments do make a difference, even of the same manufacturer and some times, the same model.
Selmer is my experience, so I can tell about. Series II is the best of them all. I have all the Alto models Selmer produces (except Series III which I did not like, but it is a great horn) and Series II is a better horn for altissimo (I have two of them and they response identically) than the Reference I have, Mark VI's I have, etc..
What I did not like about Series III (the 4 I tested and the one I bought and then sold) is that from F4 and up it did not deliver the altissimo as I like it, and I like to use those notes. Nobody says a player should, but I like to.
But, for knowing this, the altissimo has to be known, this is, being experienced, and the first notes of it, may very well come out from almost any saxophone.
My teacher, Remi Alvarez (
www.remialvarez.com) had to test several Reference 54 Tenors at Paris, France, before he decided which one to take, and the problem was with altissimo. All of them were fine horns, excelent horns, but with his fingerings, not all worked as he wanted. He is one of the best at the free jazz scene.
The advices given are very good. The reed seems soft. Need a harder reed but easy on it... develop the whole sound around the horn. Altissimo has to be added to the saxohpone, not instead of the low notes... which, may suffer from a harder reed at the beginning.
What I can tell, from fellow saxophone players, is that Yamahas are good at altissimo, but, essentially, and having it that instruments do make a difference, it is the player, not the horn.
All the best,
JI