Nope, its a not a battle to provide better search results. Its a battle of words to undermine each other with some serious accusation backed up with proof.
First it was Google to run a sting operation to provide proof to industry expert that Bing seems to be copying Google results. Details -> http://searchengineland.com/google-bing-is-cheating-copying-our-search-results-62914
Then it was Microsoft came out with allegation that top ten Google organic search results are often Spam results and 70% of those spam results are running Google Adsense giving Google indirect profit from spam. Details -> http://www.businessinsider.com/bing-engineer-accuses-google-of-profiting-off-search-spam-2011-2