Who likes meat the best?

No, donations to giants are rated by how much the donation is worth, not any particular preference of any given giant. The same donation will give you the same credit, regardless of where you donate it to.

I put together a system for determining how much a donation is worth, which can help you avoid going over the donation limits, called the FavorSaver. I haven't played the game since they un-launched it, but the tool is based on their API calls, so it should still be current (assuming they haven't changed any of the formulas).

There's some help text in the tool itself that goes into some amount of detail about how the system works. There's also this thread on the forums which may be of use.