Spartan II's - Genetic-wise naturally already better than the rest, further buffed with physical and mental teaching and training from the ages of around 5-7. These are kids who would learn calculus by the age of 10. At age 14, they had the body of an 18 year old elite level athlete.
Spartan III's - Orphans who weren't genetically awesome naturally but had the drive to get revenge. Built for high risk operations, they were suicide squads except the very best, some of whom possibly have the same Spartan II gene. They were still trained from an early age, and truly the only difference between them and SII's are cheaper armor, cheaper (But just as efficient) drugs and modifications to their body and no natural genetic that made them better.
Spartan IV's - ODST's and capable Marines would be drafted to have modifications. Because of that, most of their training were standard and they started that at the minimum age of 18, meaning that, compared to the previous 2, they missed out on about 12 years of training, of which it would have been a lot more intense. Armor and genetic enhancement drugs, etc. are even more cheaper but possibly more potent, but this still means that they didn't get it at puberty, which is when the 'big boost' really comes. The chance of one of them having the 'super-gene' that Spartan II's and possibly some Spartan III's had is there, but it is also possible that, if it is, the gene was never allowed to reach full potential.
As such, despite terrible driving, Kat is quite probably far more capable than the average Spartan IV. The only possible reason that Palmer could be better is because Palmer's parents were insurrectionists and could have been raising their child for military service.
If you were talking about which one was hawter, on the other hand.....