AP damage or not, a rear charge by dragon princes combined with the terror inducing dragon will send any combination of chosen or chaos warriors fleeing for their lives. Meanwhile, phoenix guards and swordmasters are perfectly capable of going toe to toe against chosen warriors with halberds and come out on top, and that's before you account for the loremaster supporting them.
Yeah, but as you mention your troops are getting bonuses from the LL and techs, while their Chaos counterparts aren't. This is more in terms of the multiplayer landscape, where the field is leveled (when it comes to campaign bonuses).
No issue with Swordmasters beating Chosen (Halberds), though. They really should, as any halberd unit is really more an anti-large tool, than anything else. Especially since halberd units still suffer from that annoyingly low attack interval. It would be interesting to see how they trade with the shielded/great weapon Chosen, though. On the face of it, Chosen should walk that fight. I mean, compare:
vs
SOH are more Chaos Warrior (Great Weapons) tier than Chosen (though I feel they'd beat CW reasonably well). Yes, they get a bump from that Martial Proficiency, but it's not big enough to make up that difference in armor and health (68 per model for SOH vs 108 for Chosen) and melee attack, especially.
And then there's this:
vs (on the right)
Chosen should definitely win out in both scenarios, all things being equal. Especially once their HE counterparts fall below 50% strength and lose Martial Proficiency.
All in all, seems to me like Chaos should be a tough match-up for HE. A good player will make up for the HE deficiencies, certaintly, but there you go.