I chose Eddie, simply because he was already an essential ingredient firmly entrenched in my musical being by the time Randy showed up.
On a side note, I remember when Ozzy went solo. That was a huge moment if the history of rock.
I forget when Blizzard came out, 81-83, somewhere in that area. Sabbath's core fan base, the fans that were teens in the early of Sabbath (1970), were getting on towards their 30s to mid 30s.
Ozzy, mostly likely would have kept those fans anyway, but by being shrewd enough to hire a gunslinger like Randy Rhodes, he also added a new fan base.
All those young guitarists who'd picked up a guitar because of Eddie Van Halen's work now had a new kid on the block.
Ozzy may only have a few brain cells, but he (or his people) had the business savvy to tap into the next generation.