My observations are based on unusually late model curvys: a 278k Buescher Aristocrat and a 282k Conn 4M. Differences from earlier instruments seem superficial, but there may be a few tweaks that aren't obvious. Both play in unusually good tune (I used to own a 186k Conn and the 282k is definitely easier to play in tune on the top end), and the necks are fixed at comfortable angles.
The biggest differences I find are of course tonal. The Conn is a Conn...you know at all times you're hearing a saxophone. You can lean into the sound and voice a great deal of projection and "sass" into it. At pp or ppp, OTOH, there's a slight airy resistance that's difficult to voice out. The Buescher is likewise a Buescher...its specialness is on the softer dynamics, where it can be played very delicately, with a flutelike quality. It will project beautifully too when you boot, but without quite so much extra spiciness.*
Differences in feel are interesting to consider. The Buescher is a touch lighter, so it's easier to play unstrapped, and the pivot palm keys handle just like the straight models. For some reason Conn went to stacked palm keys early in the 20s, which have to be very thinly sprung and are easier to open unintentionally. OTOH the Conn keys seem machined to closer tolerances and feel firm, where the Buescher keyboard can feel a little loose at times. The LH pinkie plates are also a little bit more of a reach on Buescher.
Bueschers to F are rare at any vintage. Serious barrel-chamber classical players have to have this exact horn. Straights, Conns, Bueschers to Eb, even the comparatively rare stencils to F such as Elkhart, are all considered inadequate. Don't go looking for a Martin branded soprano piece either - they are now standard for these players.
*It's funny because when I play the straight Bb horns, the Buescher and Conn kind of change places tonally. The straight Conn is more delicate in tone, in fact actually a little harder to voice for color. (Conn eventually created the stretch model 18M, which I find plays with a lot more character.) The straight Buescher is capable of a tangy, electric quality, which Sidney Bechet exploited to great effect.