  We present an improved numerical relativity (NR) calibration of the new
effective-one-body (EOB) model for coalescing non precessing spinning black
hole binaries recently introduced by Damour and Nagar [Physical Review D 90,
044018 (2014)]. We do so by comparing the EOB predictions to both the phasing
and the energetics provided by two independent sets of NR data covering mass
ratios $1\leq q \leq 9.989$ and dimensionless spin range $-0.95\leq \chi\leq
+0.994$. One set of data is a subset of the Simulating eXtreme Spacetimes (SXS)
catalog of public waveforms; the other set consists of new simulations obtained
with the Llama code plus Cauchy Characteristic Evolution. We present the first
systematic computation of the gauge-invariant relation between the binding
energy and the total angular momentum, $E_{b}(j)$, for a large sample of,
spin-aligned, SXS and Llama data. The dynamics of the EOB model presented here
involves only two free functional parameters, one ($a_6^c(\nu)$) entering the
non spinning sector, as a 5PN effective correction to the interaction
potential, and one ($c_3(\tilde{a}_1,\tilde{a}_2,\nu))$ in the spinning sector,
as an effective next-to-next-to-next-to-leading order correction to the
spin-orbit coupling. These parameters are determined (together with a third
functional parameter $\Delta t_{\rm NQC}(\chi)$ entering the waveform) by
comparing the EOB phasing with the SXS phasing, the consistency of the
energetics being checked afterwards. The quality of the analytical model for
gravitational wave data analysis purposes is assessed by computing the EOB/NR
faithfulness. Over the NR data sample and when varying the total mass between
20 and 200~$M_\odot$ the EOB/NR unfaithfulness (integrated over the NR
frequency range) is found to vary between $99.493\%$ and $99.984\%$ with a
median value of $99.944\%$.
