We study the distribution of electronic spectral weight in a doped antiferromagnet with various types of charge order, and compare to angle resolved photoemission experiments on lightly doped La2-xSrxCuO4 (LSCO) and electron-doped Nd2-xCexCuO4+/-delta. Calculations on in-phase stripe and bubble phases for the electron-doped system are both in good agreement with the experiment, including, in particular, the existence of in-gap spectral weight. In addition we find that for in-phase stripes, in contrast to antiphase stripes, the chemical potential is likely to move with doping. For the hole-doped system we find that "staircase" stripes, which are globally diagonal but locally vertical or horizontal, can reproduce the photoemission data with the characteristic "Fermi arcs," whereas pure diagonal stripes cannot. We also calculate the magnetic structure factors of such staircase stripes and find that as the stripe separation is decreased with increased doping, these evolve from diagonal to vertical, separated by a coexistence region. The results suggest that the transition from horizontal to diagonal stripes seen in neutron scattering on underdoped LSCO may be a crossover between a regime where the typical length of straight stripe segments is longer than the interstripe spacing, to one where it is shorter and that, locally, the stripes are always aligned with the Cu-O bonds.