Signage lighting is decided by the surrounding set-up, the kind of ambiance desired and the nature of business.
Externally-lit signages are used typically in case of huge artwork size, since the cost of internal illumination goes high. They provide an economic option with higher scope of customized artwork. They make a business outlet stand-out with respect to the competition by creating an ambiance.
Whereas internally-lit signages are sharper in appearance, because the lighting is always consistent in all the elements. Typically used in indoor settings where the surroundings are not so bright. These signages have a more modern look to them, make the brand look trendy and fashionable.
A USSC research shows that internally illuminated signage provide better long range visibility than externally illuminated signages. Link
To read more about signage design and ideas : Signage design guide