k- epsilon model poorly resolves the viscous layer unline K-Omega model. Furthermore, k-ω model is good in resolving internal flows, separated flows and jets and flows with high-pressure gradient and also internal flows through curved geometries.

The conservation equations for the turbulence kinetic energy (TKE), k (m2 s-2) and its rate of dissipation ε (m2 s-3) are calculated using k-ε standard model.

These two quantities are used to calculate the effect of the turbulence fluctuation components on the averaged conservation equations. The standard k-ε model is simple and proves to be stable in predicting flow in turbocharger compressor or other applications. In my research, although k-ε model has been used in most of the simulations, the results using RNG k-ε and k-omega models have also been examined.

The K-omega turbulence model has superior performance in terms of numerical stability in the viscous sublayer of wall-bounded flows. However, it is very sensitive to the free stream turbulence parameters, thus it is unsuitable for certain complex applications.

Standard k-epsilon The baseline two-transport-equation model solving for kinetic energy k and turbulent dissipation ε. Turbulent dissipation is the rate at which velocity fluctuations dissipate. This is the default k–ε model. Coefficients are empirically derived; valid for fully turbulent flows only. In the standard k-e model, the eddy viscosity is determined from a single turbulence length scale, so the calculated turbulent diffusion is that which occurs only at the specified scale, whereas in reality all scales of motion will contribute to the turbulent diffusion. The k-e model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. Performs poorly for complex flows involving severe pressure gradient, separation, strong streamline curvature.

Standard k-omega A two-transport-equation model solving for kinetic energy k and turbulent frequency ω. This is the default k–ω model. This model allows for a more accurate near wall treatment with an automatic switch from a wall function to a low-Reynolds number formulation based on grid spacing. Demonstrates superior performance for wall-bounded and low Reynolds number flows. Shows potential for predicting transition. Options account for transitional, free shear, and compressible flows. The k-e model uses the gradient diffusion hypothesis to relate the Reynolds stresses to the mean velocity gradients and the turbulent viscosity. Solves one equation for turbulent kinetic energy k and a second equation for the specific turbulent dissipation rate (or turbulent frequency) w. This model performs significantly better under adverse pressure gradient conditions. The model does not employ damping functions and has straightforward Dirichlet boundary conditions, which leads to significant advantages in numerical stability. This model underpredicts the amount of separation for severe adverse pressure gradient flows. Pros: Superior performance for wall-bounded boundary layer, free shear, and low Reynolds number flows. Suitable for complex boundary layer flows under adverse pressure gradient and separation (external aerodynamics and turbomachinery). Can be used for transitional flows (though tends to predict early transition). Cons: Separation is typically predicted to be excessive and early. Requires mesh resolution near the wall.

So, K epsilon is best suited for flow away from the wall, say free surface flow region, whereas k-omega model is best suited for near the wall flow region, where adverse pressure gradient is developed.

I hope this helps.