Welcome to the world of the C soprano!
There are very few of us who play these regularly (and I don't really consider myself one, to be honest), but I'll give you a bit about my experiences.
I have a Holton C soprano, one of the few keyed to high F. I would not characterize the tone as necessarily oboe-like - I think of that as being more a characteristic of a Bb soprano with a small chamber mouthpiece. I would use adjectives like "light" or "sweet".
Professor Cohen and some others have written consistently that good results on intonation are going to be hard/impossible to achieve with a Bb soprano mouthpiece and that one really needs a true C soprano mouthpiece. This has not been my experience; I have found that using either my Rousseau 4C or my Selmer S-80 C* mouthpiece on the C soprano gives me accurate intonation, within my ability as a baritone specialist to control the thing. What I mean is, I don't find tuning anomalies (individual notes way out of tune) nor trending errors (like, all the low notes get progressively sharper). I'm certainly ready to admit that Professor Cohen's standards for acceptable intonation are higher than mine; I'm positive that he's got a much better overall command of the thing to really be able to find intonation anomalies. But just coming at it from my standpoint, I really didn't notice any serious issues with those moderate-design Bb mouthpieces. I wouldn't be surprised to find problems in using a Bb mouthpiece with a tiny chamber, or one with a cavernous chamber.
Since I had to cut off the ends of both my Bb soprano mouthpieces to be able to use them on my Buescher Bb soprano, the length wasn't an issue on the Holton C. That's not uncommon anyway. And they're both relatively inexpensive mouthpieces readily replaced for short money, so I didn't hesitate to take after them with a hacksaw and files.
I love the light weight of the C soprano. I can play it for far longer than the Bb before my right thumb gives out.
The keywork is a bit odd, compared to the Bb, and keys are in slightly odd places - but that may be Holton vs. Buescher rather than Bb vs. C.
Boy is it sensitive to pitch. A voicing change that would result in a minor change of timbre on baritone will bend a note two half-steps on C soprano. It's clear to me that extensive long tone development practice would be helpful in getting a stable and precise embouchure.