After reading your post, I thought I'd try calculating the brightness difference, ignoring atmospheric absorption (figuring both would suffer equally), and possible albedo differences by wavelength, or Lambert reflection - just using flux in Watts per square meter. My equations were: Flux at Earth := (Flux at planet * Albedo * phase * area) / (distance from Earth) **2.
Values used (from aa.usno.navy.mil and nssdc.gsfc.nasa.gov) were (at 2200 UTC on June 30): Flux at Venus 2613.9 W/m**2, Albedo 0.90, Phase 0.34, Radius 6051800 meters, Distance 0.5167 AU; Flux at Jupiter 50.50 W/m**2, Albedo 0.343, Phase 0.996, Radius 69911000 meters (spherical volumetric equivalent for elliptical Jupiter), Distance 6.0755 AU.
Magnitude difference: Mv - Mj = -2.5 Log10(FEv / FEj), where FE is Flux at Earth above.
I got Mv - Mj of -4.2, or Venus appearing about 10.5 times brighter than Jupiter.
At the time, actual Mv was -4.41 and Mj was -1.64, with Venus appearing 6.96 times brighter than Jupiter.
Still not agreement, and I undoubtedly have something misunderstood, but still a fun exercise. Thanks for the excuse to play. We only saw the conjunction briefly through some clouds just after sunset here.
Hasta nebula - Chuck