I started listening to this sort of music sometime around or prior to the release of Holy Diver. I'm pretty sure Speak of the Devil was my introduction to Ozzy, but that obviously didn't include any solo material. The two Ozzy albums got no run on MTV, but Dio's Rainbow in the Dark video got a reasonable amount of airplay. Ozzy was my first rock/metal concert (Bark at the Moon tour in April 1984), and I saw Dio on the Last in Line tour later that year.
Ha! This is interesting - I wouldn't have guessed. I thought Ozzy would be more "known" outside of the more strictly hard rock/metal crowd, if anything because he was more of a crazy character (although maybe his more noteworthy shenanigans - including bat-biting and such - started later?). Dio always struck me as a more "metal" figure, cliches and all. I suppose his profile was generally higher at the time, as opposed to late 70/early 80s Ozzy, who had just been fired from Sabbath and all of that...
I can't speak with personal knowledge about '81-'82. I didn't really start listening to this sort of music until after Rhoads had died. That said, Ozzy didn't have any videos for the songs on the first two albums, which were released in '80 and '81. Dio, on the other hand, did have videos for songs on Holy Diver and Last in Line, but that's not surprising since those albums were released in '83 and '84. When I started listening, Ozzy was sort of this mythic figure. Somewhere along the way, I heard the dove and bat stories ('81 and '82 respectively), but that's really all I knew until Bark at the Moon was released in late 1983.
Ozzy as my first concert was definitely an eye-opener to a relatively sheltered 16yo me!
Rainbow In The Dark was definitely played on MTV, but so was Bark At The Moon. But then Dio released Last In Line within a year, so there was the Last In Line video. That was quite popular. But Dio at the time was never as well known as Ozzy. Ozzy was on another level of fame.
Obviously in 1986, Shot In The Dark was in heavy rotation.
That's the thing. Holy Diver/Last in Line and Blizzard/Diary don't really line up. The timeline is
April 1980 - Heaven and Hell
September 1980 (UK)/March 1981 (US) - Blizzard of Ozz
November 4, 1981 - Mob Rules
November 7, 1981 - Diary of a Madman
November 1982 - Speak of the Devil
December 1982 - Live Evil
May 1983 - Holy Diver
November 1983 - Bark at the Moon
July 1984 - The Last in Line
August 1985 - Sacred Heart
February 1986 - The Ultimate Sin
The Dio albums all had videos on MTV. Ozzy didn't start getting played on MTV until Bark, which was contemporary with the first two Dio albums. Ozzy's trajectory was rising in this time (with the obvious bump in the road that was Rhoads's death). As much as I loved his singing and persona, Dio's trajectory after Holy Diver was decidedly downward.
Like you mentioned, a LOT of stuff happened -- and happened fast -- in the first half of the '80s. The gap between the first two Ozzy albums and the first two Dio albums, while seemingly small in retrospect, seemed like a lifetime at the time.