This paper introduces a cooperative control framework based on Nonlinear Model Predictive Control (NMPC) for solving an Active Information Acquisition problem (AIA) using a system of multiple multirotor UAVs equipped with onboard sensors. The observation task of the NMPC is a minimumuncertainty pose estimation of a moving feature which is observed by the multi-UAV system, using a cooperative Kalman filter. The controller considers a full nonlinear model of the multirotors-including the motor-level actuation units and their real constraints in terms of maximum torque-and embeds the Kalman filter estimation uncertainty in its prediction. The framework allows and exploits heterogeneity in the actuation and sensing systems by considering a generic model of UAVincluding both quadrotors and tilted-propeller multirotors-and a generic model of range-and-bearing sensor with arbitrary rate and field of view. The capability of the proposed framework to reduce the cooperative estimation uncertainty of a static or a moving feature, thus leading the system to optimal sensing configurations, is demonstrated through Gazebo simulations and real experiments. The software is provided open-source.