I have a pair of lights that have a single Li-Ion battery in them and a panel that is about 4" square. Given enough sunlight during the day, these throw a decent light throughout the night. I think they are Westinghouse branded, but not sure.
The problem with these little lights is not so much the battery life, but the solar cell itself is undersized. Since it's the most expensive part of the light, it is what gets skimped on. Even with a long day full of direct sunlight there is not enough energy pumped into the battery to last the night. Adding a higher capacity battery only adds to the problem, as the battery will be perpetually undercharged, and its life shortened. That is the reason why the cheapass 500mAH NiCd cells are used. Even if the solar cell can give a full charge, having the light in any areas with shade during part of the day will leave them undercharged. Wintertime leaves even the good ones undercharged, the days are too short and the sun too low to hit the panel squarely for optimum charging.