The breakup process of a drop or a bubble immersed in a straining flow at high Reynolds numbers, is studied numerically with the aim at comparing the breakup frequencies obtained with those measured in real flows. We assume that both the inner and the outer velocity fields are axisymmetric and irrotational. Under these assumptions the time evolution of the drop's interface is computed with a boundary integral method for a wide range of the inner-to-outer density ratios, $\Lambda$. Despite the simplicity of the model, it qualitatively displays some of the features of the turbulent breakup of drops and bubbles observed experimentally. Furthermore, when $\Lambda \sim O(1)$, the slender geometry of the droplets observed in the numerical simulations suggests the use of a simplified theoretical analysis that reproduces accurately the time evolution of the drop radius obtained numerically.