Note that the diodes shown will not stand 5A. The original circuit had R3 in the wrong place, but with my change would "work" as shown, with the higher voltage drop across the transistor added to the diode drop. The diodes do the "switching" by themselves with no help from the transistors......
Your load 1 solution has revised components & count; I assume to meet application parameters and aviod smoke; however your simulation gave a result so the design "works???"................with what I percive to be 11.2v low battery overtones...
Because any idiot that knows a bit of html can put up a web page. Just because someone is computer literate enough to create a web page does not mean that they are an electronics guru... In my experience, about 80% of the circuits posted on the web are created by newbies that really cant be trusted......
If the above is true -why post the original circuit as a solution to "automatic transfer from multiple power sources".