You don't know me, but I know you.
--The Dragon Legion
In my opinion, if we were to compare the two, I would that Spartans are cooler.
1. ODST's are used for spec ops and shock infantry, or maybe even in cases of emergency.
However, they are still marines with a slightly tweaked helmet that for some reasons cause people to say that the appearance of a clothed ODST is much better than an armored Spartan with his shield generators.
2. Spartans give their life, limb, and basically their youth to fight the largest enemies of the UNSC, therefore causing the continuation of S3's when only Master Chief and a handful of other Spartan's were still alive. Yet, an ODST lives a much carefree life. He can hide behind cars and trucks while occasionally firing and waiting for MC to take care of everything. Backup support is an ODST's job in my opinion, yet I think the UNSC would still prefer Spartans.Also, ODST's are not the super enhanced fighting machines you see out there. Just some skilled Marines.
3. Spartans in my opinion can pwn ODSTs any day, even though I have it as a head for my MJOLNIR armor version.
[Edited on 08.03.2009 3:34 AM PDT]