I don't own a (commonly associated) curved hilt or one that has a gentle curve (what I imagine SFs Insurgent to be) other than my Va-Cuum Cle'Ner (which doesn't technically count).
You're wield style is the obvious difference here. With curved hilts your grip will also change. Imagine gripping a squash racquet versus gripping a tennis racket.
A squash racquet's grip is commonly nearest the very top of the grip-wrap with your thumb and forefinger simulating a gentle 'V'. The dueling style is most associated with a fencing style also.
A tennis racquet's grip is commonly nearest the very bottom of the grip-wrap (relative to just above the pommel) with a virtual closed fist straightened.
You've mentioned in other threads that you lean towards or establish your grip and wielding style from oriental weaponry much like the katana. This can sometimes combine the two mentioned above liking to say gripping a golf club. However it becomes a dual-hand wield which isn't as comfortable on a curved-hilt.
To go single handed grip on a curved, you'll be essentially going through an 'unlearning' exercise to train short swings, slashes and more stabbing motions.
For fluidity of movement during dueling, the single handed curved demonstrates more refinement and control. The blade is swung as it is directed. Compared to a straight hilt, still consistent to aforementioned, your motions tend to be guided by the swings in a more exaggerated way than above.
That's my interpretation.
Thought the PS was your next decisive moment?