(Not a teacher)it ought to look awkward:"Bruno is on on side and Shmuel on the other side of the fence"
my friend told me that it should be
it ought to look awkward:"Bruno's on side of the fence and Shmuel on the other".
It's hard to tell if a lot of this is just typo and missing words through typing...
The first is more correct because 'one' is there (you wrote 'on', but I assume it was a typo). However, neither are correct.
It seems your friend was just contracting the verb 'be', which isn't more or less correct. But he missed 'one' (again, maybe a typo) - you can't have just "Bruno is on side of the fence".
Also, in both sentences, it would be better to have the verb 'be' for Shmuel as well.
As for 'of the fence' - I don't think it matters grammatically which clause (Bruno, or Shmuel) takes this phrase. However, from an inference point of view, saying it in Bruno's clause seems less ambiguous.
So a correct sentence would be: "Bruno is (Bruno's) on one side of the fence and Shmuel is (Shmuel's) on the other."