mobile battery charging using voltage regulator?
The Instructables circuit is horrible and shouldn't be used.  It:


has none of the required capacitors for the regulator.
lacks the resistive dividers on the D+ and D- lines to make the phone enter proper charge mode
runs off a battery with about 10% the capacity of a phone battery.


All in all the whole idea of the circuit is idiotic.

The other circuit seems to be aimed at directly charging a battery rather than supplying power to a device with a built in charge circuit (like a phone).  I'm not quite sure what they're doing with a 555 in there.

It certainly isn't suitable for connecting up to a 5V power input on a phone. It looks like it may blow the phone up.

To charge a phone from batteries you need:


Regulated 5V power
Enough current (500mA minimum)
Enough battery capacity to get a decent charge
For USB charged devices the D+ and D- lines require specific voltages on them to enter charge mode


Neither of those circuits provide that.