There are a lot of differences between student horns and professional horns. I'll list two easy ones:
* The professional horn from any manufacturer will be made to their highest quality with their highest quality materials. That doesn't mean that one company's professional horn is better than another's, it just means it's the best they can make.
* The professional horn will help you shape your own sound easier than a student horn.
The difference in tone quality can generally be heard by playing the horns one after the other or "side-by-side." Student horns generally have a bit "brighter" and "thinner" tone. However, if you're going to ask me to pick out the Buffet R13 from a group of 30 other clarinets playing
at the same time, I doubt I can.
FWIW, there should be equal importance given to the mouthpiece. A really nice mouthpiece can make a really average clarinet sound quite nice, as I've demonstrated for years when I played student and intermediate horns with a pro mouthpiece.
The #1 determinator of how you sound is you. It doesn't matter if you have the world's best horn and world's best mouthpiece if you aren't a good player.
Looping back a bit, the player can tell a lot more about the horn than the listener. "This horn is really easy to play altissimo on!" "This horn has much more convenient keywork." Etc. Also note that horns tend to have their own little quirks, too, like, "The low Eb is 5 cents sharp, so I have to furrow my brow to get it to play in tune." There's also the pragmatic: "This horn plays the upper altissimo very nicely, but it's $5000 more than this other horn that does a pretty good job." Of course, if a horn is easier to play, you'll probably want to play more, which will make you into a better player
.