LTC4415 or LTC4413

Hi, I am currently looking for a switch of some sort to decide which power to send to the load based on the voltage differences from each input.

I have 2 capacitors that are being charged. I want CAP1 to be the main source. They will be 3V caps and when CAP1 falls below 2V, I want to switch to CAP2 and either if CAP2 falls below 2V or if CAP1 gets to 3V, switch back to main power of CAP1. Will the LTC4415 or LTC4413 work for my application?

For the LTC4415, if the caps falls below 1.7, the device will shutdown correct? And same for the LTC4413 at 2.5V?