Auto-switching Power Mux with High Current Output for 5V Power Sources
Use can two schottky diodes, and a SPDT relay. In this way, during the relay switch time, the output voltage won't drop too much, without needing a big capacitor. Once the contact has been established, you get a very low voltage drop, and no dissipation on the diodes.

Remember that relays have different ratings between NO and NC contacts. The NC contact have smaller ratings.

I guess that you can use diodes with smaller ratings than 6A, as they just operate for a very small time (check the datasheet for peak forward current!).

Alternatively, you could use an hysteretic comparator, which drives two MOSFETs.







simulate this circuit &ndash; Schematic created using CircuitLab