I started out using an AP2112. That is the same one as on the (new) Huzzah.
Have a TP4056 feeding/charging a LiPo cell. I feed the TP4056 with a 6 Volt Solar panel. TP4056 goes to an AP2112 that delivers a nice 3.3 Volt (dropvoltage 125mV at 300mA). Have to be a bit careful with the AP2112 as it can only take 6V max.
As I saw the HT7333 recommended left and right I tried that too. I am not sure what the dropvoltage of that one is at a decent current, it is 90-100mV at 40mA, which is a low current, but the ESP8266 operated well while sending I didnt measure the voltage (I may do so) as it was operating well. The HT7333 is available in a TO92 I think which makes it a bit more attractive to solder.
Also tried the RT9013. That is the same one as on the Wemosboard. Works well in the circuit described above.
I have to add that it hasn’t been very sunny, but as as my LiPo remained charged above 3.7 everything functioned well. Still got to see what happens if it drops to 3.3 Volts, but I presume that will be OK too as I have fed an ESP8266 with 3 Volts and it worked well.
considering prices USD
AP2112 = 18.5 cts
HT7333 = 12.5 cts
RT9013 = 16 cts
XC6203 = 23.8 cts
I think I may stick to the AP2112. Let me add though that it has an enable pin that needs to be pulled high through a 10k resistor. Could consider that a nuisance or an option.
The HT7333 is handy if yr eyesight isnt that great but considering the datasheet doesnt give much info for higher currents I guess I will just leave it.
Maybe slightly letting the topic creep: I also tried a Wemos battery shield which I directly fed (through the USB port) with a 6V solarpanel and a battery attached (darned different connectors).
That actually works well and is an easy way of solar feeding the Wemos D1 mini