Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially two-dimensional) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in three dimensions, we conduct a comprehensive particle-in-cell simulation study comparing two- and three-dimensional evolution of long, thin current sheets in moderately magnetized, collisionless, relativistically hot electron–positron plasma, and find dramatic differences. We first systematically characterize this process in two dimensions, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths and system sizes. We then show that three-dimensional (3-D) simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3-D current sheet evolution is not always fundamentally classical reconnection with perturbing 3-D effects but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in two dimensions. Intriguingly, non-thermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in two and three dimensions. Although the variety of underlying current sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.