Originally Posted by va_cyclist
Panniers are better for heavy loads like water and whatnot, because they keep the center of gravity lower and closer in to the bike frame. Your wobble may be coming from a high center of gravity, and there's not a lot you can do about it. Panniers are also better than an open basket at protecting packed clothes from the elements.
Panniers really seem nice, but they are somewhat cost-prohibitive.
I switched from the home made trunk bag to baskets specifically to lower the center of gravity. Before, I was riding with everything in the bag, over the back wheel. Now everything is down, below the top rim of the back wheel and I am using a waterproof bag for my clothes.