It's slightly more complicated than that. If I'm not mistaken :
RAV : Both Serah and Noel will learn the spells up to -ara (if I'm correct - I'm playing the French version, I'm not familiar with the terminology of the English one), and all the -impact. However, only Serah will be able to cast Thundaga and Firaga, whereas Noel will be able to cast Aeroga and Blizzaga. Both learn the same passive abilities, but not at the same time.
Serah will learn the spells quicker than Noel, who is stuck with Blizzard/Aero/Ice-impact/Aero-impact for a while.
COM : I "think" they learn the same abilities, but once again not at the same time. Also, Serah will unlock Ruin² quicker than Noel, and being more Magic-oriented she will be a better COM than him when it comes to inflict magic damages.
SOI : Noel is a better healer than Serah, learning all the spells (including the group ones), whereas Serah can't. However, healing is influenced by the Magic stat, so Serah is a better single-target healer than Noel. However, Noel can heal the whole party, so in the end Serah tends to lag behind. To be honest, they aren't that great as healers
TAC (Tacticien ; Synergist) : Same as above. Noel > Serah, by far.
DEF : Both will learn usefull abilities. However, Noel can't learn Steel Guard, whereas Serah can (as odd as this seems).
SAB (Saboteur ; Jammer in english I think) : Serah is better than Noel, period.
So, to sum up all this :
- Serah's "main" jobs : COM (Magical), RAV (Better than Noel early on), SAB
- Noel's "main" jobs : COM (Physical), RAV, SOI, TAC
Both are decent Defenders.