Treating IMU measurements as inputs to a motion model and then preintegrating these measurements has almost become a de-facto standard in many robotics applications. However, this approach has a few shortcomings. First, it conflates the IMU measurement noise with the underlying process noise. Second, it is unclear how the state will be propagated in the case of IMU measurement dropout. Third, it does not lend itself well to dealing with multiple high-rate sensors such as a lidar and an IMU or multiple asynchronous IMUs. In this paper, we compare treating an IMU as an input to a motion model against treating it as a measurement of the state in a continuous-time state estimation framework. We methodically compare the performance of these two approaches on a 1D simulation and show that they perform identically, assuming that each method's hyperparameters have been tuned on a training set. We also provide results for our continuous-time lidar-inertial odometry in simulation and on the Newer College Dataset. In simulation, our approach exceeds the performance of an imu-as-input baseline during highly aggressive motion. On the Newer College Dataset, we demonstrate state of the art results. These results show that continuous-time techniques and the treatment of the IMU as a measurement of the state are promising areas of further research. Code for our lidar-inertial odometry can be found at: https://github.com/utiasASRL/steam_icp