  Sr_2CuO_3 and Ca_2CuO_3 are considered to be model systems of strongly
anisotropic, spin-1/2 Heisenberg antiferromagnets. We report on the basis of a
band-structure analysis within the local density approximation and on the basis
of available experimental data a careful analysis of model parameters for
extended Hubbard and Heisenberg models. Both insulating compounds show
half-filled nearly one-dimensional antibonding bands within the LDA. That
indicates the importance of strong on-site correlation effects. The bonding
bands of Ca_2CuO_3 are shifted downwards by 0.7 eV compared with Sr_2CuO_3,
pointing to different Madelung fields and different on-site energies within the
standard pd-model. Both compounds differ also significantly in the magnitude of
the inter-chain dispersion along the crystallographical a-direction: \approx
100 meV and 250 meV, respectively. Using the band-structure and experimental
data we parameterize a one-band extended Hubbard model for both materials which
can be further mapped onto an anisotropic Heisenberg model. From the
inter-chain dispersion we estimate a corresponding inter-chain exchange
constant J_{\perp} \approx 0.8 and 3.6 meV for Sr_2CuO_3 and Ca_2CuO_3,
respectively. Comparing several approaches to anisotropic Heisenberg problems,
namely the random phase spin wave approximation and modern versions of coupled
quantum spin chains approaches, we observe the advantage of the latter in the
reproduction of reasonable values for the N\'eel temperature T_N and the
magnetization m_0 at zero temperature. Our estimate of $J_{\perp}$ gives the
right order of magnitude and the correct tendency going from Sr_2CuO_3 to
Ca_2CuO_3. In a comparative study we also include CuGeO_3.
