Compton imaging or Compton camera imaging has been studied well, but its advantages in nuclear medicine and molecular imaging have not been demonstrated yet. Therefore, the aim of this work was to compare Compton imaging with positron emission tomography (PET) by using the same imaging platform of whole gamma imaging (WGI). WGI is a concept that combines PET with Compton imaging by inserting a scatterer ring into a PET ring. This concept utilizes diverse types of gamma rays for 3D tomographic imaging. In this paper, we remodeled our previous WGI prototype for small animal imaging, and we developed an image reconstruction method based on a list-mode ordered subset expectation maximization algorithm incorporating detector response function modeling, random correction and normalization (sensitivity correction) for either PET and Compton imaging. To the best of our knowledge, this is the world's first realization of a full-ring Compton imaging system. We selected 89Zr as an imaging target because a 89Zr nuclide emits a 909 keV single-gamma ray as well as a positron, and we can directly compare Compton imaging of 909 keV photons with PET, a well-established modality. We measured a cylindrical phantom and a small rod phantom filled with 89Zr solutions of 10.3 MBq and 10.2 MBq activity, respectively, for 1 h each. The uniform radioactivity distribution of the cylindrical phantom was reconstructed with normalization in both PET and Compton imaging. Coefficients of variation for region-of-interest values were 4.2% for Compton imaging and 3.3% for PET; the difference might be explained by the difference in the detected count number. The small rod phantom experiment showed that the WGI Compton imaging had spatial resolution better than 3.0 mm at the peripheral region although the center region had lower resolution. PET resolved 2.2 mm rods clearly at any location. We measured a mouse for 1 h, 1 d after injection of 9.8 MBq 89Zr oxalate. The 89Zr assimilated in the mouse bony structures was clearly depicted, and Compton imaging results agreed well with PET images, especially for the region inside the scatterer ring. In conclusion, we demonstrated the performance of WGI using the developed Compton image reconstruction method. We realized Compton imaging with a quality approaching that of PET, which is supporting a future expectation that Compton imaging outperforms PET.