Electrical

My 95 Prism has an electrical problem. It can go from full charge and everything working at top performance to 1/2 power or less. My lights will go dim for a few minutes then all of a sudden they are full brightness again. I have changed out the battery and the same thing happens. I put my old battery in my Toyota and it works great. I have an auto start, I was wondering that that could be a problem. Or do you know what the problem could be? Thnx