Recent experiments by Burton and Taborek have demonstrated a droplet-to-bubble transition in the pinchoff behavior of one inviscid fluid inside another. With D the relative densities ρ(E)/ρ(ℑ), they find transition from (D=0) droplet-to-bubble behavior at D≈4. Numerical simulations of this two-fluid system, up to and beyond the initial breakup of the inner fluid, have been carried out utilizing level set and boundary integral methods. A droplet-to-bubble transition is predicted: For D sufficiently large, the volume of the satellite droplet shrinks to zero and there is no overturning of the fluid at separation. The calculated self-similar scaling exponents and the pinchoff region shapes match the known behavior at the droplet and bubble extremes (D=0, D=100). For intermediate D values, the simulations presented here indicate that the transition range between droplet and bubble behavior depends upon initial drop geometry. When the neck separates two nonequal inner fluid masses the transition is mild and occurs in the range 4<D<10, whereas in the case of equal masses an abrupt transition occurs at D≈4 in perfect agreement with the above mentioned experiments.