With Mario as the standard, Luigi's various Jumps are higher and longer, but he skids farther when coming to a dead stop after running. That said, Green Stache is a monster at using the Cloud powers to get past portions that give Red Stache hell in the same circumstances.

If you cannot make a good jump for a certain portion as Mario, you can do it better as Luigi.
If you need precision for a pit-laden path, Mario is the plumber/doctor/referee/too-many-jobs-to-list for the job.

The trick is knowing when to hit the gas (Luigi) and ease up on the throttle (Mario) with the daily platforming skills.