Scott - It's hard to generalize about fish diets, because they can change from place to place, and across months. However, here goes.
Golden shiners primarily feed on zooplankton. They can, in some times and places, also eat aquatic stages of insects, such as chrinomids (midges or bloodworms) and other insects. At times, they can even have quite a bit of filamentous algae in their diets, although I'm not sure if they are eating it on purpose, or taking it in while feeding on zooplankton or insects.
Gizzard shad can at times (not always) really be tough on a pond fish community. If a pond gets a high density of large gizzard shad (they can reach 2 pounds and larger, and there can be hundreds of pounds per acre of water), it REALLY suppresses the food production for you sport fish. They also don't reproduce very much when there is a high density of adults, and then they produce few prey-size fish for the predators. An easy example of problems is bluegills -- bluegill growth and size invariably decline when gizzard shad are introduced.
Also, the young (age-0 or that year's hatch) gizzard shad grow very quickly, and often outgrow young predators. For example, gizzard shad often will be 4 inches long by August, and most largemouth bass hatched that year can no longer feed on them (too big to swallow).
So, I'd say those were the primary differences. Golden shiners are just a lot more vulnerable to predators, and with even a moderate largemouth bass density, I wouldn't expect high population density for the goldens. The only place I've seen excessive numbers of golden shiners that probably were causing a problem was in a trout impoundment.
Hopefully, we can get a few other folks to provide some comments on this subject. In my experience (which is not as broad as some other people on this site), the goldens can be a good choice for an additional prey source in a bass pond.
Dave