We analyse the linear stability and nonlinear evolutions of circular hetons under the quasi-geostrophic approximation. We compare results obtained with a three-layer model and with a model based on a continuous density stratification. Though the models also differ by the vertical boundary conditions, they show a remarkable similarity in the stability properties of the hetons (threshold values of vortex radius for baroclinic instability, dominant modes, growth rates, etc.), and in their nonlinear evolutions (spatial reorganization of potential vorticity by nonlinear processes, end-states of the simulations). The hetons prone to baroclinic instability often break into two hetons drifting in opposite directions, and in more hetons, for wider initial structures. In both models, instability is quite sensitive to the vertical gap between the opposite-signed vortices: as it increases, the instability decreases and shifts to lower azimuthal modes. Finally, though modes l ≥ 2 (i.e. elliptical and shorter wave deformations) prevail in most of the parameter space, the mode l = 1 perturbation (a vertical tilt of the vortex column) exists for hetons with small vertical gaps. Such perturbations are concentrated vertically near the gap, and can only be evidenced in the continuously stratified model.