The fight for bragging rights between the United States’ two main stock exchanges, the New York Stock Exchange and Nasdaq, assumed an even sharper edge in the past week.

After Nasdaq OMX issued a press release claiming the most new listings of any U.S. exchange, NYSE Euronext, the Big Board’s parent, took the unusual step of sending out a note to journalists refuting Nasdaq OMX’s calculations and asking them not to repeat Nasdaq’s boast.

And this week, the Big Board sent out a detailed letter to clients challenging line by line some of Nasdaq’s market share claims.

Here is an excerpt from the letter:

The most recent boasts by one of our competitors, NasdaqOMX, takes a turn from William  Shakespeare’s “A Midsummer Night’s Dream,” the romantic comedy that seeks to blend  identities and blur the lines of fantasy and reality.  For good reason, the competitor’s  dramatic escapade calls for a real world response.

The letter then proceeded to refute a number of Nasdaq OMX claims, not least of which is its share of the trading of NYSE-listed shares, a sore spot for NYSE.

Of course it’s hard for third parties to know which figures submitted by the exchanges are comparable, with all the various acquisitions they’ve made and platforms they’ve developed.

And it’s not the first time the exchanges have gotten snippy with each other.

At an industry conference in June, Nasdaq OMX Chief Executive Robert Greifeld told the audience his exchange had that day for the first time traded more NYSE-listed stocks than the NYSE itself. When it was NYSE Euronext CEO Duncan Niederauer’s turn a few speakers later, he could hardly contain his irritation at his rival’s boast.

But the whole Nasdaq-NYSE battle may be moot. The real fight is not just with each other. Now the two are competing with overseas exchanges like Deutsche Börse trying to get a foothold in the U.S., with each other abroad, and with exchanges that trade in other kinds of assets, like futures and options.

What’s more, upstarts like BATS Trading and Direct Edge have wasted no time taking away 15 percent of their business in just a couple of years.

NYSE’s letter to its clients concluded thus:

We are fully committed to making our market centers the most competitive and most
customer-friendly.  We welcome your input and greatly appreciate the opportunity to
serve you and your constituents.  And while open to factually challenging the       creative imagination of our competition, we promise to spare you the Shakespearean
drama.

    A little goodwill goes a long way. Toss in $112 million, and it could even seal a multi-billion-dollar deal that was looking about as sure as a five-day weather forecast.

    CME Group, the world’s top derivatives exchange, and NYMEX Holdings, the energy and metals market it wants to buy, responded to the complaints of NYMEX membership by tossing $138,000 more at each of the 816 Class A member seats. To top it off, NYMEX officials from the CEO on down graciously agreed to reduce their “change of control” payouts, helping shave $30 million off the transaction cost — and helping to lower the spears of members that threatened to fell the deal for months.    

A sprinkle of sugar and the bluster is all but gone.    

Analysts lined up Friday to agree with CME Executive Chairman Terry Duffy, who said he was “very comfortable” the takeover will now succeed.

“There’s probably still some ill will there, but this goes a long way toward healing their wounds,” Deutsche Bank North America analyst Robert Rutschow said of the rift between NYMEX management and some members, who have been saying the CME’s offer was too low. Now, CME looks all but assured to get the 75-percent support it needs from members, especially after one of the most vocal dissenters among them, Bobby Sahn, came around on Friday.

For CME, NYMEX represents round two of its bruising battle to expand in the fast-moving world of exchanges. Last year, the company forked over $4 billion more than it had originally offered for the Chicago Board of Trade, the hand of which IntercontinentalExchange also longed for at the time. The NYMEX affair, now all but a done deal, should prove softer on CME’s wallet — particularly as tumbling CME shares decrease the deal’s overall price tag.  (By Jonathan Spicer)

(Photo, by Reuters of CME S&P 500 trading pit)