An all in 1 single mosfet ideal diode device supporting up to 5 amps & 9-26v:
http://www.analog.com/media/en/technical-documentation/data-sheets/4358fa.pdf0.025 ohm on resistance, so, if you draw 1 amp, expect a voltage drop of 0.03v, not a pitiful schottky 0.4v. That's more than an order of magnitude of improvement.
Now, for the top 2.5v-5.5v device, this one has 2 ideal mosfet diodes in 1 ic package, however, it has a 0.12v drop at 1 amp, but there is a bonus digital output indicator of which power source is currently in use & and it has an over voltage protection:
http://www.analog.com/media/en/technical-documentation/data-sheets/441312fg.pdfOk, for now I will stop with the ideal diodes, but, if you need it, they do have versions at different voltages and currents, and versions for use with external mosfets where you can get your voltage drop down to 0.01v, but with additional caveats.
Now, hint, there is an even better all in one diode in a TO-220 package designed for reverse bias protection or serialization of solar panels in the above 40 amp range, but, it does have a small continuous pulse switching time caveat & it's pricey, but I'll let you google that one if you need such a fancy device.