B737 FLT CREW DEPARTING RWY 19L AT LAS REPORTS CONFLICT WITH B757 ON GO AROUND FROM RWY 25L NEAR ROPPR INTERSECTION.

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DEPARTING LAS ON RWY 19L; AT APPROX 100 KTS IN THE TKOF ROLL; I SAW ANOTHER CARRIER B757 IN AN OBVIOUS MISSED-APCH CLB FROM RWY 25L (I ASSUME THAT WAS THE RWY). I TOLD THE FO HE WAS GOING TO BE A FACTOR ON THE CLB. WE CONTINUED THE TKOF (I WAS PM) AND GOT THE GEAR RETRACTED. TWR CALLED AND SAID TO MAINTAIN 6000 FT ON DEP INSTEAD OF THE 7000 FT WE HAD BEEN CLRED TO INITIALLY FOR THE SHEAD DEP; OAL TRANSITION. OUR FIRST FIX WAS FIXIX; OFF THE END OF THE RWY. THE OTHER CARRIER SHOULD HAVE BEEN GOING TO '3000 FT; THEN A R TURN TO 6000 FT DIRECT THE BLD VOR AND HOLD' IF HE HAD BEEN DOING THE PUBLISHED MISSED APCH FOR RWY 25L. SINCE I COULD NOT HEAR THE INSTRUCTIONS ISSUED HIM ON FREQ 119.9 (WE WERE USING 118.75); I DIDN'T THINK HE WOULD BE A GREAT DEAL OF TROUBLE FOR US; AS I FLY INTO LAS FREQUENTLY AND KNOW THE MISSED APCH FOR RWY 25L IS A R TURN AWAY FROM US. INSTEAD; HE WAS ISSUED 7000 FT ON DEP AND EITHER A RADAR VECTOR TO TURN TOWARD US OR HE WAS FLYING TO THE FIXES ASSOCIATED WITH THAT RWY FOR A NORMAL DEP; WHICH WOULD BE PIRMD AND ROPPR. WE WERE INFORMED OF HIS CLB TO 7000 FT BY BOTH THE TWR AND DEP CTL; BUT HE DID NOT CLB EXPEDITIOUSLY TO THAT ALT. AS WE CLBED OUT OVER FIXIX TO MAKE THE TURN TO ROPPR; I COULD SEE HE WAS GOING TO BE A FACTOR (I HAD HIM VISUALLY AND ON THE TCAS) AND I TOLD THE FO TO SLOW THE CLB RATE. WE WERE CLBING AT ABOUT 4000 FPM AND HE SLOWED IT TO 2000 FPM. PASSING 5500 FT; I COULD SEE THE OTHER CARRIER HVY TURNING INTO US AND NOT MUCH HIGHER THAN WE WERE; SO I TOLD THE FO TO STOP THE CLB; WHICH HE DID AT 5800 FT. THE OTHER CARRIER HVY PASSED OVERHEAD OUR ACFT AND BEHIND US AT ABOUT 7000 FT ABOVE US AND LESS THAN A HALF MI FROM US. THE CTLR CLRED US TO 7000 FT; THEN 11000 FT AND WE CONTINUED THE DEP ON THE SID. IN MY ESTIMATION; THE CAUSE OF THE NEAR MISS (AND THAT IS HOW I WOULD CHARACTERIZE IT) WAS THE OTHER CARRIER'S SLOW CLB RATE TO AN ASSIGNED ALT. BUT MORE IMPORTANTLY TO THE AIR TFC CTLRS IN CHARGE OF THIS SITUATION; AS THEY ISSUED INSTRUCTIONS.