Laser plasma accelerators (LPA) offer an exciting possibility to deliver high energy, high brightness electrons beams in drastically smaller distance scales than is typical for conventional accelerators. As such, LPAs draw considerable attention as potential drivers for next generation light sources and for a compact linear collider. In order to asses the viability of an LPA source for a particular application, the brightness of the source should be properly characterized. In this paper, we present charge dependent transverse emittance measurements of LPA sources using both ionization injection and shock induced density down ramp injection, with the latter delivering smaller transverse emittances by a factor of two when controlling for charge density. The single shot emittance method is described in detail with a discussion on limitations related to second order transport effects. The direct role of space charge is explored through a series of simulations and found to be consistent with experimental observations.