Sage doesn't really use SymPy a whole lot. Most of the core algebra in Sage is based on C libraries like MPIR, Flint, Singular, Pari...
Nemo uses some of the same libraries under the hood, but there's much less overhead. This is in part due to Julia being faster than Python (although Sage works around that to some extent by using Cython), and in part due to Nemo using tighter algorithms/code.
Note that Nemo is currently more geared towards purely algebraic computation, though. It doesn't currently have S-expressions with support for symbolic integration and the like (Sage mostly uses Pynac and Maxima for this).
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They have a benchmarks page where it compares quite favorably to SageMath. I don't know but I'd kinda assume that Sage uses Sympy under the hood.
Sage doesn't really use SymPy a whole lot. Most of the core algebra in Sage is based on C libraries like MPIR, Flint, Singular, Pari...
Nemo uses some of the same libraries under the hood, but there's much less overhead. This is in part due to Julia being faster than Python (although Sage works around that to some extent by using Cython), and in part due to Nemo using tighter algorithms/code.
Note that Nemo is currently more geared towards purely algebraic computation, though. It doesn't currently have S-expressions with support for symbolic integration and the like (Sage mostly uses Pynac and Maxima for this).