Omnivores lack the specialist behaviour of carnivores and herbivores, searching widely for food sources, and are thus better able to withstand changes within their ecological niche, which is at the top level of trophic chains :)

André Panis Associated Scientist at French National Research Institute

For many orders or species of insects it is true. However I observe in the Mediterranean granivorous ant Messor barbara, if workers don't encounter seeds to bring to the nest, they can enter within their nest with a dead body of their own species or of another ant species in its mandibules. 

Too many species and habitats to answer precisely?

Omnivores species can exploit /utilizes wider niche in a habitat therefore more generalist that specific feeders. More over trophic ranges area also wider that make omnivores as generalist feeders.

Omnivores use much variety of habitats. Foraging behaviours are higher than that of herbi and omni.