Emerging applications for positron emission tomography (PET) may require the ability to image very low activity source distributions in the body. The performance of clinical PET scanners in the regime where activity in the field of view is <1 MBq has not previously been explored. In this study, we compared the counting rate performance of two clinical PET/CT scanners, the Siemens Biograph Reveal 16 scanner which is based on lutetium oxyorthosilicate (LSO) detectors and the GE Discovery-ST scanner which is based on bismuth germanate (BGO) detectors using a modified National Electrical Manufacturers Association (NEMA) NU 2-2007 protocol. Across the activity range studied (2-100 kBq/mL in a 5.5 mL line source in the NEMA scatter phantom), the BGO-based scanner significantly outperformed the LSO-based scanner. This was largely due to the effect of background counts emanating from naturally occurring but radioactive 176Lu within the LSO detector material, which dominates the observed counting rate at the lowest activities. Increasing the lower energy threshold from 350 keV to 425 keV in an attempt to reduce this background did not significantly improve the measured NECR performance. The measured singles rate due to 176Lu emissions within the scanner energy window was also found to be dependent on temperature, and to be affected by the operation of CT component, making approaches to correct or compensate for the background more challenging. We conclude that for PET studies in a very low activity range, BGO-based scanners are likely to have better performance because of the lack of significant background.