Microfluidic devices have recently been demonstrated as an effective platform for generating monodisperse drops and bubbles, which is important for applications from emulsification to drug delivery and lab on a chip. Here we compare drop formation mechanisms in microfluidic devices in which flows can be either predominantly shear flows, or predominantly elongational flows. In either case, drops of an aqueous liquid form due to viscous stresses imposed by a second oil phase. We show that the two flow types lead to dramatically different ability to control droplet sizes. We characterize the drop size over a large number of experiments by varying capillary number, volume fraction, and viscosity ratio. We observe distinct breakup modes depending on these three dimensionless parameters, and the flow type.