Zero echo time (ZTE) and ultrashort echo time (UTE) pulse sequences for MRI offer unique advantages of being able to detect signal from rapidly decaying short-T2 tissue components. In this paper, we applied 3D ZTE and UTE pulse sequences at 7T to assess differences between these methods. We matched the ZTE and UTE pulse sequences closely in terms of readout trajectories and image contrast. Our ZTE used the water- and fat-suppressed solid-state proton projection imaging method to fill the center of k-space. Images from healthy volunteers obtained at 7T were compared qualitatively, as well as with SNR and CNR measurements for various ultrashort, short, and long-T2 tissues. We measured nearly identical contrast-to-noise and signal-to-noise ratios (CNR/SNR) in similar scan times between the two approaches for ultrashort, short, and long-T2 components in the brain, knee and ankle. In our protocol, we observed gradient fidelity artifacts in UTE, and our chosen flip angle and readout also resulted in shading artifacts in ZTE due to inadvertent spatial selectivity. These can be corrected by advanced reconstruction methods or with different chosen protocol parameters. The applied ZTE and UTE pulse sequences achieved similar contrast and SNR efficiency for volumetric imaging of ultrashort-T2 components. Key differences include that ZTE is limited to volumetric imaging, but has substantially reduced acoustic noise levels during the scan. Meanwhile, UTE has higher acoustic noise levels and greater sensitivity to gradient fidelity, but offers more flexibility in image contrast and volume selection.