I don't remember anyone from one show being on the other. Stargate is another we've binge watched. Been a few years now so maybe we'll watch it again later this year.
The Stargate series had several main actors from Firefly
Morena Baccarin played Inara in Firefly played Adria in SG-1’s tenth season.
Jewel Staite played Kaylee in Firefly and played a female Wraith and Dr. Jennifer Keller in Stargate Atlantis.
Ben Browder played John Crichton on Firefly and Lt. Colonel Cameron Mitchell on SG-1
Claudia Black played Officer Aeryn Sun on Firefly and Vala on Stargate Atlantis