LiPo + charge/boost circuit vs pre-built "power bank" - contrasting portable power sources
The thing to remember with power banks bought on places like eBay and Amazon is:


THEY LIE ABOUT THE CAPACITY


A typical power bank you would expect to get around 3600mAh from, even though it may say 10000mAh, 50000mAh, 1,000,000,000,000mAh, etc.

The only technical difference between rolling your own circuit and a power bank is the low-current switch-off that many (but not all) of them have.  That switch-off is fine if you are always drawing a good amount of current, but once your device goes to sleep and the current drops right down you'll find the power bank will switch off and your device will never wake up again.

However, with rolling your own system you know what you are getting. You know the capacity of your battery.

One further thing to consider: Do you really need 5V? The majority of electronics run from 3.3V nowadays, and the Arduino is no different. There are Arduino boards designed to run from 3.3V, and even 5V boards can be tweaked to run at 3.3V (albeit slower than normal).

So the ideal solution would be:


A single-cell Li-Poly / Li-Ion giving nominal 3.7V
A Li-Ion charger circuit
A low-dropout or switching regulator with max 400mV dropout.


And no boost circuit needed. Also, no logic level shifting when communicating with 3.3V devices.