We present the analysis of the full shape of anisotropic clustering measurement from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS), re-analysed using an updated recipe for the non-linear matter power spectrum and the non-local bias parameters. We obtain constraints for flat Lambda cold dark matter cosmologies, focusing on the cosmological parameters that are independent of the Hubble parameter h. Our recovered value for the Root Mean Square (RMS) linear perturbation theory variance as measured on the scale of 12 Mpc is sigma(12) = 0.805 +/- 0.049, while using the traditional reference scale of 8 h(-1) Mpc gives sigma(8) = 0.815 +/- 0.044. We quantify the agreement between our measurements and the latest cosmic microwave background data from Planck using the suspiciousness metric, and find them to be consistent within 0.64 +/- 0.03 sigma. Combining our clustering constraints with the 3 x 2pt data sample from the Dark Energy Survey Year 1 release slightly degrades this agreement to the level of 1.54 +/- 0.08 sigma, while still showing an overall consistency with Planck. We furthermore study the effect of imposing a Planck - like prior on the parameters that define the shape of the linear matter power spectrum, and find significantly tighter constraints on the parameters that control the evolution of density fluctuations. In particular, the combination of low-redshift data sets prefers a value of the physical dark energy density omega(DE) = 0.335 +/- 0.011, which is 1.7 sigma higher than the one preferred by Planck.