According to Diamond, people domesticated plants before they domesticated mammals.
One way to see this is to look at Tables 9.3 and 5.1. These give the dates for earliest attested dates of domestication. Table 5.1 tells us that domestication occurred in Southwest Asia by 8500 BC. Meanwhile, Table 9.3 tells us that sheep and goats were first domesticated in 8000 BC. This shows that the plants must have been domesticated first.
However, the domestication of animals did help to improve the cultivation of domesticated plants. Diamond tells us in Chapter 4 that the domestication of large animals helped to increase crop production because of such things as animals' ability to pull plows and their production of manure that could be used as fertilizer.
Diamond tells us, then, that plants were domesticated first, but that the domestication of animals also helped to make plant domestication more economically productive.