Given that Ozzy is a mess...however,
Black Sabbath's first incarnation came about in the late 60s and early 70s. Back when everyone was talking about love and peace and hippy shit, they were talking about war, death, and the apocalypse.
When Dio joined the group, he had already made waves in another of the early great metal bands with Rainbow. The second incarnation of Black Sabbath was pretty much a melding of the two bands and allowed everyone to see how great the music was. The late 70s and early 80s were not devoid of great hard rock acts and no one was really making waves - Judas Preist, Blue Oyster Cult, etc. Black Sabbath II was just a way to keep metal in the high profile. It didn't have as many iconic songs to recall save for "Neon Knights" and the aforementioned "Heaven and Hell." However, when you say "War Pigs," "Iron Man," "Sweet Leaf," and "Paranoid" everyone immediately knows them.
I say comparing Ozzy and Dio are like comparing apples and oranges. They both are metal icons and are deserving of whatever is laid at their feet, even if Ozzy has become a parody of himself. But do to the outstanding evidence of influence, ground breaking music, and recognition - Ozzy's version clearly, for me, wins this battle.