When we expand into outer space, we may contact other sapient species, and it can be guaranteed that they will think differently than us. But we may be able to predict their behavior by their diet. Something that Larry Niven touched on with the carnivorous Kzinti and the herbivorous Puppeteers.
Carnivores: The first thing you should remember is that predators are opportunists, they always take the route that is least expensive. If they get to colonizing other planets I would expect them to have the capability to adapt considering their need for complex ecosystems that would be a hassle to terraform from scratch. Due to their opportunistic natures I doubt that they might go to the trouble of eating other sapient species like us humans, though if there is a massive technological difference they might enslave or domesticate the less advanced species. Relations with humanity would probably be neutral or even allies, we might colonize and terraform dead worlds while they adapt to living ones.
Herbivores: To an herbivore, any other animal is a potential enemy, a predator or a competitor. I expect that their planets would be ecological disasters devoid of any other animal species except in the most extreme regions they never got around to colonizing. Since their supporting ecosystems would be comparatively simple they would probably terraform their colonies, because of that I expect that they would use a lot of weapons of mass destruction in inter-species wars. In addition the fact that extreme paranoia would have been a survival trait in their early history (more than humans anyway) would make diplomacy with them very difficult.
Omnivores: Would probably be closest to humans psychologically, as we are omnivores ourselves. Kind of a wild card, they might terraform, they might adapt, they might exterminate, they might enslave. They might even join forces with us and form the galactic federation. Fortunately trends on earth make it seem like most sapient species will be omnivorous.
Plants: I don't see any reason for plants to become sapient, but maybe a machine civilization would be similar. In short, they wouldn't care about consumers unless we got in their way.