How the hell did you come up with this after I was thinking about it earlier today?
It would probably be horrific... not even for the unnecessary deaths that would almost definitely happen, but because it would send the world spiraling into a pit of doubt, second-guessing, and confusion.
Alright. All creatures on the planet, big or small, are now as intelligent or almost as intelligent as human beings, right? And they would, potentially (if biologically possible) develop a way to communicate with others, or we would discover a way to communicate with them.
Now everyone must be completely aware of every other living thing (sans flora) at all times. That bug you just stepped on by accident? Murder. That hamburger you're going to eat? Murder. The leather you're about to wear as a belt or put in your pocket as a wallet? Also murder.
I, for one, don't think that this is currently the case (as many vegetarians/vegans might lead you to believe), but if it was the case, it would be chaos. People, adults and children alike, would be stricken with grief by the accidental deaths of sentient insects. We would question whether or not owning animals or using them for milk and eggs (we likely would quickly stop eating meat, which would cause severe shortages of food all over the world) is slavery. Do we pay the animals? Do they consider the food and shelter we give them significant enough to justify this? Or do they want something more?
Also, how will animals represent themselves? Will they have cultures? Will they develop societies of their own? How will they cooperate (or not cooperate) with humanity?
Humanity may be nearing seven billion on the planet, but animals outnumber us significantly.
I think it would be disastrous for a very long time, until all people (human and animal alike) were educated as soon as possible to respect and acknowledge all life. Smaller lifeforms (insects, rodents, etc.) would likely be forced to live in protected areas to make certain they don't get accidentally stepped on or killed.
I think everyone who is trying to say that, "Oh, animals are already intelligent! They already have feelings and individual thought!" isn't quite taking into account the bigger picture. ALL animals. ALL of them. And HUMAN levels of intelligence, or at least close. The change would be noticeable very quickly, or so I would hope.
I hope it never happens. I like eating meat, and I don't want the deaths of thousands of intelligent bug-people on my conscience.
EDIT: Oh, and we'd probably have to find a way for carnivorous animals to stop eating herbivores and the like. Because, you know, equality and all that jazz. People don't eat other people.