Resolution augmented with the rule of symmetry or the rule of extension
First, ER p-simulates SR: for example, ER is p-equivalent to the extended Frege proof system (EF) which is p-equivalent to the substitution Frege proof system (SF), and it is easy to see that SF p-simulates SR (the symmetry rule amounts to substitution of a special kind).

On the other hand, Urquhart [1] proves an exponential lower bound on SR refutations of Tseitin tautologies for certain graphs. Since Tseitin formulas have polynomial-size ER (or extended Frege) refutations, this shows that ER is exponentially more powerful than SR.

Reference:

[1] Alasdair Urquhart: The symmetry rule in propositional logic, Discrete Applied Mathematics 96–97 (1999), pp. 177–193, doi: 10.1016/S0166-218X(99)00039-6.