Sorry for my late arrival to this post, but as I read through all the entries, I felt the need to add my own thoughts. I have been playing saxophone and oboe professionally as well as teaching both instruments for many years. First thought, the fact that someone told you you sound like an oboe does not give you any real information. The oboe can sound many ways just as the saxophone can. Developing oboists often sound bad and play with poor intonation, just as with the saxophone, but professional level oboe players produce gorgeous sounds. In the classical arena, a great oboe sound can often have soprano-like qualities and vice versa, and this should not surprise us. Performers on both instruments tend to strive for consistent tonal balance, and clear, colorful, warm sounds. Additionally, both instruments have a conical bore and nearly the same range. In fact, the saxophone and the oboe are more closely related acoustically than the sax and the clarinet.
Sound concept was mentioned briefly earlier, but it is the key point here. How do you want to sound? You must develop your sound concept, your mental image of the way you want to sound. This will guide every other decision you make including equipment choices. Realize, though, that certain sounds are inappropriate in certain contexts. Sounding like Kenny G in a sax quartet playing Bozza isn’t likely to go over very well. I think you mentioned that you play in a sax quartet. In that case, go listen to Prism, Zyzyx, etc. The US Army Field Band Saxophone Quartet is a very fine ensemble, and they have many YouTube videos that can help you get started. Additionally, listen to the great classical soloists play soprano: Rousseau, Sugawa, Murphy, Tse, McCallister, etc. They often record oboe pieces on soprano, BTW.
If you want to play mainly play jazz soprano, again who do you want to sound like? Liebman? Koz? Kenny G? There are many, and you need to find the sound where you want to start.
I happen to disagree with the open throat/warm air concept, but that is for another time. The point of having good throat control and plenty of air support was well made and spot on.