I may be Apple certified, but will say there is no official guidance on whether one is better or not.
This is a long running debate. Note it is possible to overcharge a logicboard, and a flush of the logicboard sometimes is necessary to get the machine started again. This typically is more due to the power manager not working properly.
But that's a hardware issue for a certified tech to examine.
It is wise to only use the proper wattage for the proper computer. Use a magnifying glass if necessary to read the AC/DC brick of notebook power cords to find the wattage and check the specs of your notebook computer. Also check for signs of fraying of any cables. Many people wind the cables too much around the L shaped clasps, and for power cords that are not separate from the AC/DC part of the power cord, can easily get damaged if bent too much at the entry point. When there is fraying that's when powering the computer can be problematic. If you find the cord is frayed, immediately replace it.
Batteries tend to age after they are more than 2 years old, and http://www.apple.com/batteries/ has guidance on how to charge them.