What are the differences between the War Mage and the Sorceress

+1 to Kelox for the grinder, as this is by far the most effective way to deal with both kobolds and sappers. However, because of their short range, they are not always an option, so here are a few other options:

• Tar pits. The tar pits slow kobolds down to about the speed of a normal orc, which slows them down enough for your other traps to hit them. These are especially effective with the ceiling-mace - a single ceiling-mace with tar-tiles below it will kill all kobolds and weak/medium orcs (and heavy orcs, with upgrades) if you can force them to walk along the length of the mace, leaving only trolls/ogres to deal with.
• Barricades + Grinders. If the hallway is too wide, you can force enemies to walk near the grinders using barricades. Note that this only works in a level without sappers, as sappers will destroy the barricades.
• Traps with long range will hit them when placed parallel to their movement (rather than perpendicular like usual). For instance, place arrow-traps on the wall they face just before they turn a corner.
• Archers are extremely good at taking out smaller enemies like Kobolds and Sappers. They're only useful when they can be placed far enough away that they won't be attacked. Also, be wary on levels with Gnoll Hunters, as they will go out of their way to kill your Archers.
• Kill them manually. If you are good at shooting, get a fast-shooting weapon (like the sorceress's staff, or the crossbow) and take them out yourself. And if your aim isn't so good, using the alchemist's satchel (which does splash in a large radius) can be very effective in taking out large groups of kobolds - made even more effective with tar-pits, since the kobolds will group up

The shock-zapper and brimstone will also kill them, but (as you found out) are not particularly effective at it.

I saw an approach where cross-bow/stone-staff, wind-belt and morph-ring were the primary weapons and the traps taken were push-traps, spring-traps, haymakers(or zappers) , barricades, brimstones (for sappers and runners), coin-trincket and one extra trap/trinket(cant remember correctly).

This strategy is kinda tricky and there are huge risks involved.
The first few levels, you will see yourself windbelt-ing the orcs into the lava pit (tough to get money this way). The core essence of this strat is to have haymakers in the bridge-zone (bridge?) with some damage dealing trap (probably the one that i forgot - scorcher may be). The rest of the path till this will be laid with push-traps and spring traps facing the pit, so that the small ones fall into the pit and the bigger are taken care by the primary attack plus the haymaker+scorcher combo.
The bridge ares is the only kill box you can have with no barricades. I mentioned barricade in the list above since some of the orcs will fall in the side-walk area and then take that path to the rift. Some people prefer to block the side paths so that they walk back considerable distance and then go thro the traps again. May be, the barricade can be skipped in favour of steam-trap/ice-vent for slow (or tar in case of warmage, but then you wont get the morph-ring). Place the brimstones at the beginning of the opening and just before the rift, so that if runner/sappers come first they get burned instantly. If not, let them escape and the last brimstones will take of that.

Surviving this way will be very tough. Let me know how it goes (I failed at it :D ). If you succeed please make a video and share. Hope this helps!. Happy killing orcs