I’d never heard of MIST or Greenhand courses required for working offshore, nor known anyone with them.
MIST appears to be an ADDITIONAL course offered on top of the standard survival.
http://www.opito.com/index.php?option=com_content&task=view&id=164&Itemid=99
They are aiming for everyone to have completed it by 2010, so probably worthwhile for people to do it now, however I would wait until I actually had a JOB! No point in laying out money for a course in an industry that you may not get a job with and it will count for nothing in any other job!
The MIST scheme allows for companys own in-house safety training to be certified as MIST training, so I wouldn’t bother doing it and just wait till you do your own employers one (cos you nothing then).
Greenhand training appears to be an Offshore Drilling safety initiative.
http://www.opito.com/library/industry_training_standards/offshore_drilling_industry_green_hand_standard.pdf
It is not a requirement to have in order to work offshore, just a "nice to have". It seems to be combined more with a Banksman/slinger training so is possibly more aimed at rig deck crew and not appropriate for ROV people.
Out of the 2 scheme, I would suggest if you wish to do one, the MIST would be more appropriate as it appears it will possibly be made more of a requirement to have by 2010.