Transistor UPS circuit
Do you need to use switching transistors?  You can accomplish the same switching by using just two diodes.  Select the diodes to safely pass the highest amount of current expected, and the diode's reverse voltage to withstand the highest voltage expected.  (Including a fuse on the battery side is also a good investment in case of any problems.)  .See below. 







simulate this circuit &ndash; Schematic created using CircuitLab