We put a Falcon SS system on our BN2; I thought it sounded tinny at first, but as it got carboned-up it mellowed out some.
The argument for SS, besides looking shiny--IMO it distracts from the rest of the car (because the exhaust is so visible on a Big Healey)--is that it will outlast mild steel. Maybe so for a grocery-getter, but most of us don't fire up the Healey unless we're going to take a real drive, like 10 miles or more. That gives the system a chance to heat up and evaporate the moisture from condensation, limiting rust. I bought an Ansa system for my BJ8 over 30 years ago and still use the pipes, though I've spliced-in 'Heartthrob' mufflers (sourced from J. C. Whitney). Since most of the systems are of the shredded fiberglass/metal packing variety, the stuffing gets blown out before the metal rusts (I've heard this about the 'Tourist Trophy' SS systems Moss sells). I think the OEM mufflers were stuffed, but I've never been able to confirm it. On a Healey, you're likely to bash the system to unusable before they rust through.
AHSpares has a mild steel system FS:
> Austin Healey Exhaust System <