Traditional Neon signs are made by forming a glass tube to the shape of the logo or text, filling it with Neon gas then igniting it with a high voltage applied at each end. They can be cheaper than LED signs but can only be formed once. If the text changes you throw it away!
LED signs are more versatile, rather than being pre-formed characters, they normally use a matrix of LEDs which can be either turned on or off the make the font and characters you want. They use fairly complicated electronics and sometimes thousands of LEDs though so the price might be higher.
There is an attractive compromise that might be worth considering: You use a sheet of glass over a black background and surround it's edge with UV LEDs. The UV light isn't visible to the eye except for a pale purple color but if you write on the glass with flourescent marker pen, the writing glows brightly. It means you manually clean it and write new text if necessary but has the advantage of allowing any art you can draw and in any color you can get from the marker pen.
Brian.