EMB135 FLT CREW FAILED TO GIVE WAY TO OTHER ACFT AS INSTRUCTED BY ATC. OTHER FLT STOPPED TO AVOID COLLISION.

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AFTER LNDG RWY 22R WE CLRED THE RWY AT TXWY C. THE FO ASKED ABOUT CALLING OPS FOR THE GATE; BUT I INSTRUCTED HIM TO WAIT UNTIL WE WERE ACROSS ALL RWYS. WHILE I WAS SAYING THIS WE WERE INSTRUCTED TO CROSS RWY 27L; GIVE WAY TO AN AIRBUS AND CONTACT GND ON TXWY B. THIS CAUSED ME TO NOT HEAR THE PART ABOUT GIVING WAY. WE ACKNOWLEDGED THE CLRNC TO CROSS; AND CONTINUED OUR TAXI AFTER LOOKING DOWN THE RWY; WHICH APPEARED TO BE CLR. I THEN HEARD THE CTLR ADD '...AND GIVE WAY TO THE AIRBUS.' I THEN SAW THE TAXIING AIRBUS AND WE BOTH STOPPED. I BELIEVE I DIDN'T SEE HIM BECAUSE OF THE BLIND SPOT CREATED BY THE POST BTWN THE 2 L COCKPIT WINDOWS; AND THE GLARE OF THE SUN WHICH WAS IN LINE WITH US. AFTER STOPPING I ELECTED TO CONTINUE ACROSS THE RWY BECAUSE WE APPEARED TO BE PARTIALLY IN FRONT OF THE AIRBUS AND I BELIEVED IT WOULD BE BEST TO CLR THE RWY AS EXPEDITIOUSLY AS POSSIBLE. AFTER RECEIVING CLRNC TO THE GATE THE GND CTLR ASKED ME TO CONTACT THE TWR SUPVR. AFTER PARKING I CALLED THE TWR AND WAS TOLD THAT THEY WERE LOOKING INTO THE INCIDENT; BUT LATER TOLD ME THAT THERE WOULD BE NO FURTHER ACTION TAKEN ON THEIR PART; AS IT WAS NOT A RWY INCURSION; BUT A TAXI DEV THAT RESULTED IN NO SERIOUS EVASIVE ACTION. IT SHOULD BE EMPHASIZED TO FLT CREW MEMBERS THAT ATC COMS AND RWY AWARENESS HAVE A MUCH HIGHER PRIORITY THAN ROUTINE COMPANY COMS. WHEN LNDG ON THE N SIDE OF ORD THERE IS PLENTY OF TIME TO GET GATE INFO; EVEN WHEN ATC REQUESTS IT. BOTH PLTS NEED TO REMAIN 'HEADS UP' UNTIL IT IS SAFE TO MAKE LESS IMPORTANT RADIO CALLS; EVEN IF VERY CLOSE TO THE GATE. I WILL BE INCLUDING THIS CONCEPT IN MY BRIEFINGS FROM NOW ON. ACTIVELY CLRING THE RWY PRIOR TO ENTERING ALSO NEEDS TO BE EMPHASIZED. I SAW FIRST HAND HOW EVEN A LARGE ACFT CAN EASILY BE MISSED. SUPPLEMENTAL INFO FROM ACN 764057: FAILURE TO FOLLOW ATC INSTRUCTIONS BY A COMMUTER EMB135. WE WERE ROLLING OUT RWY 27L ISSUED INSTRUCTIONS TO CLR AT 'C' INTXN. RJ WAS ISSUED INSTRUCTIONS TO GIVE WAY TO AND FOLLOW US AT 'C' CONTACT GND WHEN CLR. RJ DID NOT GIVE WAY OR STOP RESULTING IN AN IMMEDIATE STOP AVOIDING GND COLLISION. CAPT OF THE RJ HAD SUN VISOR DOWN AND DID NOT SEE OUR ACFT.