The Sydney Approach North controller was radar vectoring MAC 60193, a USAF military transport aircraft, to intercept the flight planned track to Christchurch after departing from RAAF Richmond. VH-CZC was being radar vectored by the Sydney DEPARTUREs North controller to intercept the 002 radial to West Maitland after taking off from runway 25. When it became apparent that the flight paths would conflict, the DEPARTUREs North controller was assigned the task of maintaining adequate separation between both aircraft. The minimum separation required was 1000 ft vertically, or 3 nautical miles laterally. A climb restriction was applied to VH-CZC, limiting that aircraft to an altitude of 6000 ft. This restriction was applied in anticipation of MAC 60193 reaching 7000 ft or higher before lateral spacing was less than 3 nautical miles. However, for a period of about 3 minutes, the C141 failed to climb as rapidly as the DEPARTUREs controller had anticipated and it became apparent a traffic confliction could not be averted. Both crews were notified of the conflicting traffic and given heading changes. Visual contact was established and the aircraft passed safely clear of each other at less than the minimum required separation standard.