While the dual Lumatek 600 240v only has 1 power cord - it has 2 cordsets (ofcourse) AND 2 power switches. 1 power switch controls 1 cordset - the other the 2nd cordset.
That being said - if one goes out- you'll be down 2 lights instead of 1...and if anything is going to fail - its going to be one of those cheap power switches.
Go with 2 seperate ballasts..price difference isnt that huge of that dually...and they are more reliable because they have no switch to fail. The 240v 600w lumateks rock. I have 12 I can vouch for their reliability.. they are tiny and run cool.
EDIT - just re -read the post.. they MUST run on the same schedule...because they only have 1 power cord.
EDIT - you can however run just 1 of the 2 600s if you wanted to.