The original version of the DS Lite originally featured bigger screens.
In an "Iwata Asks" segment about the DSi LL, the team behind the latest version of the DS has confirmed that at one point, the original DS Lite design had bigger screens in addition to its brighter displays. The size of the screens was going to be 3.8 inches, bigger than the standard DS Lite screens but smaller than the DSi LL screens.

The high demand for the DS Lite in Japan was such that the updated DS Lite was put on hold. But the technology found in that model made its way to the DSi LL, according to the designers.
In addition to the details behind the DSi LL's creation, the team also mentions how they thought of many names before they chose DSi LL for Japan and DSi XL for North America and Europe. Shigeru Miyamoto suggested the name DSi Deka, Japanese for DSi Large. Other suggested names included DSi Executive, DSi Comfort, DSi Premium, and DSi Living.