A B727-200 FLT IS TOLD TO ABORT THEIR TKOF FROM RWY 13 WHEN ANOTHER ACR FLT IS ON A 2 MI FINAL FOR RWY 4 WHICH WAS SENT AROUND AT LGA; NY.

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CLRED FOR TKOF RWY 13 AT LGA (USUAL LNDG TFC FOR XING RWY 22; ON APCH ABOUT 2 MI OUT). AS OUR TKOF BEGAN; LGA TWR ASKED US TO DISCONTINUE THE TKOF AND HOLD SHORT OF RWY 22. THEY ALSO REQUESTED RWY 22 LNDG TFC GO AROUND; WHICH THEY DID. AS WE WERE MOVING NO MORE THAN AN ESTIMATED 20 KTS; WE COASTED TO A GENTLE STOP; SHORT OF RWY 22; WITH LITTLE IF ANY BRAKING. USUAL ANNOUNCEMENTS MADE TO PAX CONCERNING A DISCONTINUED TKOF; AND WE EVENTUALLY WERE RESEQUENCED AND WENT ON OUR WAY; ONLY AFTER APPROPRIATE PROCS AND CHKLISTS REVIEWED AS WELL AS INFORMATIVE ANNOUNCEMENTS MADE TO PAX. WE FELT THE BEGINNING OF OUR TKOF HAD ADEQUATE SPACING ON THE LNDG TFC. BUT; THE SYS AND CONCEPT OF TRYING TO ACCOMMODATE AIR TFC DEMANDS IS STRAINED FOR BOTH PLTS AND CTLRS ALIKE; SO IF ONE OF THE 'TEAM' FEELS THE NEED TO TAKE THE SAFE SIDE; IT'S BEST TO DO SO. FRANKLY; I FEEL THE ATC SYS IS AT ITS LIMIT; BOTH ON THE ARPT AND IN THE AIR. WHO WILL HAVE THE STRENGTH TO SAY 'ENOUGH!' (AM FLYING OUT OF LGA; A LOT! IT'S A 'HOT SPOT!') LITTLE 'MARGIN' IS LEFT FOR TYPICAL HUMAN ERROR OR JUST COMMON SENSE FLEXIBILITY TO REALITY OF PROBS (COM GLITCH; AN EMER OR ACFT ABNORMAL PROB; ETC).