Autonomous exploration of unknown space is an essential component for the deployment of mobile robots in the real world. Safe navigation is crucial for all robotics applications and requires accurate and consistent maps of the robot's surroundings. To achieve full autonomy and allow deployment in a wide variety of environments, the robot must rely on on-board state estimation which is prone to drift over time. We propose a Micro Aerial Vehicle (MAV) exploration framework based on local submaps to allow retaining global consistency by applying loop-closure corrections to the relative submap poses. To enable large-scale exploration we efficiently compute global, environment-wide frontiers from the local submap frontiers and use a sampling-based next-best-view exploration planner. Our method seamlessly supports using either a LiDAR sensor or a depth camera, making it suitable for different kinds of MAV platforms. We perform comparative evaluations in simulation against a state-of-the-art submap-based exploration framework to showcase the efficiency and reconstruction quality of our approach. Finally, we demonstrate the applicability of our method to real-world MAVs, one equipped with a LiDAR and the other with a depth camera. Video available at https://youtu.be/Uf5fwmYcuq4 .