Small animal positron emission tomography (PET) is a well-established imaging modality in preclinical biomedical research. But depth encoding detectors are required to simultaneously achieve high spatial resolution and high sensitivity for a small animal PET scanner. In this work, we evaluated several dual-ended readout detector modules using lutetium oxyorthosilicate (LSO) arrays with crystal sizes ranging from 0.70 mm to 0.44 mm, read out by either position-sensitive avalanche photodiodes (PSAPDs) or position-sensitive silicon photomultipliers (PS-SiPMs). A new type of PS-SiPM was developed recently and was evaluated for the first time in this work. First, the signal-to-noise ratio (SNR) of both PSAPDs and PS-SiPMs was measured, and then the flood histograms, energy resolution and depth of interaction (DOI) resolution of dual-ended readout detector modules by using both PSAPDs and PS-SiPMs were measured. The PSAPD has much better SNR as compared with PS-SiPM. For the detectors using PSAPDs, crystals as small as 0.44 mm can be resolved and a DOI resolution as good as 1.4 mm was obtained. For the detectors using PS-SiPMs, 0.7 mm crystals can be resolved and a DOI resolution of 2.9 mm was obtained. Based on the results of the flood histograms, energy resolution and DOI resolution the detector modules using PSAPD are better than those using PS-SiPMs. The SNR of the PS-SiPM would need to be improved to resolve even smaller crystals and the number of SiPM cells also need to be increased to reduce the saturation effect to improve the DOI resolution. The performance of the three dimensional depth encoding PET detectors using PSAPDs is much better because the SNR of PSAPD is much higher than PS-SiPM. In the future, high resolution depth encoding PET detectors will be developed by using both new PS-SiPMs and SiPM arrays.