The difference between the songs is the groove/feel.
Black Sabbath started off as a blues band and blues songs are built on grooves and swing feels. As history tells us, the guys saw a horror movie being played across the road from their rehearsal space and decided to write songs that scared people. But no matter how low they tuned, they still kept the swing groove/feel from the blues in the process.
So when Ozzy decided to cover some Black Sabbath songs for the “Blizzard Of Ozz” tour, he picked some of the classics, like “Paranoid”, “Iron Man” and “Children Of The Grave”. And from reading a few bios, Randy Rhoads (RR) was against covering these songs, as he didn’t want the project to be an extension of Ozzy’s previous band.
Regardless, “Children of The Grave” with Randy Rhoads (RR) is a stand out. RR ignored the triplet swing feel that Sabbath had on their “Masters Of Reality” version and went straight for the metal tempo feel of 146 beats per minute. RR also refused to tune down, so he fretted the C#m note instead of playing it as an open string the way Iommi does. By doing this, it allowed RR to me more precise with his picking and little melodic motifs.
And there is no doubt in my mind that by learning to play some of the Sabbath songs, RR used em all as influences for “Over The Mountain”.
If you don’t believe me, check out the Black Sabbath riff just before the “Over the Mountain” solo. And RR plays the intro/verse riff of “Over The Mountain” more or less the same as he plays “Children Of The Grave”. The only difference being, “Children of The Grave” is in C#m and “Over The Mountain” is in G#m.
And the solo break that RR throws in for the outro, made me want to learn the song. It starts from 3.15 and ends at 4.40.
There is also a little nod to all of the blues players from about 3.56, as RR plays a standard blues lick that even Ace Frehley used in “Love Gun”.
One song doesn’t take away from the other and both songs stand on their own.
If you want groove, then Black Sabbath’s version is for you. If you really like the NWOBHM and the LA Scene, then the live Ozzy/RR version is for you.