  In this paper we present data from 72 low redshift, hard X-ray selected AGN
taken from the {\it Swift}-BAT 58 month catalogue. We utilise spectral energy
distribution fitting to the optical to IR photometry in order to estimate host
galaxy properties. We compare this observational sample to a volume and flux
matched sample of AGN from the EAGLE hydrodynamical simulations in order to
verify how accurately the simulations can reproduce observed AGN host galaxy
properties. After correcting for the known +0.2 dex offset in the SFRs between
EAGLE and previous observations, we find agreement in the SFR and X-ray
luminosity distributions; however we find that the stellar masses in EAGLE are
$0.2 - 0.4$ dex greater than the observational sample, which consequently leads
to lower sSFRs. We compare these results to our previous study at high
redshift, finding agreement in both the observations and simulations, whereby
the widths of sSFR distributions are similar ($\sim0.4-0.6$ dex) and the median
of the SFR distributions lie below the star forming main sequence by
$\sim0.3-0.5$ dex across all samples. We also use EAGLE to select a sample of
AGN host galaxies at high and low redshift and follow their characteristic
evolution from $z=8$ to $z=0$. We find similar behaviour between these two
samples, whereby star formation is quenched when the black hole goes through
its phase of most rapid growth. Utilising EAGLE we find that 23\% of AGN
selected at $z\sim0$ are also AGN at high redshift, and that their host
galaxies are among the most massive objects in the simulation. Overall we find
EAGLE reproduces the observations well, with some minor inconsistencies ($\sim$
0.2 dex in stellar masses and $\sim$ 0.4 dex in sSFRs).
