The description of realistic strongly correlated systems has recently advanced through the combination of density functional theory in the local density approximation (LDA) and dynamical mean field theory (DMFT). This LDA+DMFT method is able to treat both strongly correlated insulators and metals. Several interfaces between LDA and DMFT have been used, such as (N-th order) Linear Muffin Tin Orbitals or Maximally localized Wannier Functions. Such schemes are however either complex in use or additional simplifications are often performed (i.e., the atomic sphere approximation). We present an alternative implementation of LDA+DMFT, which keeps the precision of the Wannier implementation, but which is lighter. It relies on the projection of localized orbitals onto a restricted set of Kohn-Sham states to define the correlated subspace. The method is implemented within the Projector Augmented Wave (PAW) and within the Mixed Basis Pseudopotential (MBPP) frameworks. This opens the way to electronic structure calculations within LDA+DMFT for more complex structures with the precision of an all-electron method. We present an application to two correlated systems, namely SrVO3 and beta-NiS (a charge-transfer material), including ligand states in the basis-set. The results are compared to calculations done with Maximally Localized Wannier functions, and the physical features appearing in the orbitally resolved spectral functions are discussed.