Epstein-Zin (EZ) preferences are a generalisation of dynamic CRRA preferences.
In standard CRRA preferences, i.e.
$$
U(c_0,\dots) = \mathbb{E} \left[ \sum_t \beta^t \frac{c_t^{1 - \rho}}{1 - \rho} \right]
$$
The Arrow-Pratt relative risk aversion is $\rho$ and elasticity of intertemporal substitution is $\frac{1}{\rho}$ and thus is unable to be disentangled.
EZ solves this. Actually, the representation you have above is only for deterministic streams. EZ preferences have the recursive representation:
$$
V_t = \left( (1-\beta)c_t^{1-\rho} + \beta \left[ \mathbb{E} V_{t+1}^{1-\alpha} \right]^{\frac{1-\rho}{1-\alpha}} \right)^{\frac{1}{1-\rho}}
$$
Where $\alpha$ captures risk attitudes and $\rho$ the elasticity of intertemporal substitution.
In fact, they agree on deterministic streams of consumption (i.e. when there is no uncertainty). Take a (non-stochastic) stream $(c_0,c_1, \dots)$ and the expectation operator drops to
$$
V_t = \left( (1-\beta)c_t^{1-\rho} + \beta V_{t+1}^{1-\rho} \right)^{\frac{1}{1-\rho}}
$$
Define the monotone transform $U_t = V_t^{1-\rho}$ to get
$$
U_t = (1-\beta)c_t^{1-\rho} + \beta U_{t+1}
$$
in other words
$$
U_0(c_0,c_1,\dots) = (1-\beta) \sum_t \beta^t c_t^{1 - \rho}
$$
which are just CRRA!