Are deterministic and nondeterministic Cellular Automata equivalent?
I think you should define precisely what you mean by equivalent, and
possibly what kind of CA you are willing to consider, with what
communication grid. So I will just assume the simplest interpretation.

Given that it is fairly easy to build deterministic cellular automata
with Turing power (even with a 1 dimemsional grid), and that according
to the current wisdom of the Church-Turing Thesis, we have little
chance to improve on that, my best bet is that non-deterministic
cellular automata cannot be more powerful than deterministic
ones. Given that adding non-determinism can only increase the
computational power, i.e. a deterministic automaton is a special case
of non-determinism, whe should not expect non-deterministic cellular
automata to be less powerful than deterministic ones.

Hence, in terms of computational power, deterministic and
non-deterministic cellular automata are equivalent.