I guess you are talking about PET imaging systems which are based either on BGO or LSO (or LYSO) scintillations (the ones based on other types e.g. BaF are not common now).
LYSO has mostly better parameters (faster, more light) but much more expensive than BGO. BGO has slight advantage on density and Z number, much cheaper but produces much less light and slower.
The coincidence window that can be used with BGO has to be wider, so they need to be used at lower activity, cannot be really yet used in Time-Of-Flight reconstruction mode. However, lower cost of BGO often allows to have twice as much detection area in the system as compared to LSO(LYSO) and that may give overall advantage in performance.
Dear Hesham; i think this publication can be useful for your question. "Comparison of LSO and BGO block detectors for prompt gamma imaging in ion beam therapy " DOI: 10.1088/1748-0221/10/09/P09015