To be honest I don't think there is any real issue here regarding similar films from the two animation stables and disagree with anyone who thinks there are more than two comparable sets of films in the original question.
Firstly, we can eliminate two of your examples, as Dreamworks were not involved (The Wild, Robots), so perhaps the question could be made more general - this then negates the alleged 'conflict'.
Also, Flushed Away was an Aardman production before Dreamworks came on board as a distribution partner.
In fact, the only films that show any resemblance to each other are A Bug's Life (which was a remake of Seven Samurai) and Antz (which was an semi-original story), and Finding Nemo and Shark Tale, which share nothing else other than being set under the sea.
Is it well known that there are occasional years when live action releases seem to follow a similar theme (Armageddon/Deep Impact, Volcano/Devil's Peak, Snow White and the Huntsman/Mirror, Mirror, even this year with Olympus has Fallen/White House Down). In most cases this is down to coincidence, or one production company rushing to get their version out before the other, thus affecting the release dates.
Pixar and Dreamworks have no reason to copy each other. The amount of time and money invested in any given animated feature is phenomenal and both companies know that merely copying the other (or even entertaining the fake notion that there is a rivalry between the two houses) does them no favors.
In fact, Pixar went so far as to scrap one of their future releases, Newt, due to possible conflicts with other productions. Some industry insiders believe it was the similarity of the story to Blue Sky's Rio, others attribute it to the success of Rango (ILM) with Pixar not wanting to turn out 'another' lizard/amphibian flick.
You can see some of the concept art for Newt at the Pixar Wiki page.
Bottom line: the similarities are few and far between and these can be put down to coincidence.