The dynamical and structural properties in two ionic liquid electrolytes (ILEs) based on 1-ethyl-3-methylimidazolium bis-(trifluoromethanesulfonyl)-imide ([emim][TFSI]) and N-methyl-N-propylpyrrolidinium bis-(trifluoromethanesulfonyl)imide([pyr13][TFSI]) were compared as a function of lithium bis-(trifluoromethanesulfonyl)-imide (LiTFSI) salt concentrations using atomistic molecular dynamics (MD) simulations. The many-body polarizable APPLE&P force field has been utilized. The influence of anion polarization on the structure of the first coordination shell of Li(+) was examined. In particular, the reduction of the oxygen of the TFSI anion (OTFSI) polarizability from 1.36 Å(3) to 1.00 Å(3) resulted in an increased fraction of the TFSI anion bidentate coordination to the Li(+). While the overall dynamics in [pyr13][TFSI]-based ILEs was slower than in [emim][TFSI]-based ILEs, the exchange of TFSI anions in and out of the first coordination shell of Li(+) was found to be faster in pyr13-based systems. The Li(+) ion transference number is higher for these systems as well. These trends can be related to the difference in interaction of TFSI with the IL cation which is stronger for pyr13 than for emim.