I am pretty sure Vergir archer from peasant line can be countered by spear-man and sniper from Rhodok's peasant line.
Each Veagir archer has 1 Ivory bow or yew strong bow, 1 pack of Ivory arrow(30-40 I am not sure), 1 one hand weapon, 1 shield.
In siege battle, not against Rhodok, 1 wave of Ivory archers can kill about 100 men on garrison before running out of ammo.
Normally, ordinary shield can take 1-3 shot from Vergir archer before it breaks, however, rhodok shield can take about 6 shots or more.
Rhodok sniper has a crossbow that now does 80 damage per shot (former 100), with shield and crossbow they should be able to win Veagir archer.
Choosing Khergit first seems to be a hard choice. Their best unit is lancer troop, they are not designed for charging but fighting against other cavalry units. If your Khergit units fight on rough hill terrain or siege against Veagir you will lost for sure until you can access noble troop. Veagir noble troops and Veagir archer from peasant line are not much different. Veagir archer has shield but low ammo to begin with and Vegir noble troops has more ammo but no shield, however, Veagir archer is easy to mass than the noble one.
The same difficult goes for Swadian and Nord. Nord has disadvantage as always because they rely on infantry which is just normal troop, no matter how they have more status points or not they can not use many tactics in battle due to their limits.
Swadian peasant line troops also has disadvantage. Generally, Swadian is good because of their heavy cavalry, while the highest peasant line of Swadian troops can have only medium armor hunter horse which still has bad charging power. No matter how powerful their armor is, if Swadian units are on ground they will likely be dead sooner than you always expect.
Back to Khergit, they are, well, directly, weak. They still move too slow and attack too slow to match the damage power and accuracy of Veagir archer. If you charge Veagir lord, you can expect your lost at least 10 or whole army.
In siege battle, of course, it is pretty much suicide. Khergir has no counter against accuarcy and damage power of Veagir archer at all.
I used Veagir archer before. They are easy to mass. to kill 100 enemies in each battle then retreat and charge again until win, it is so easy, until much later in game when you fight against charger knights. You can use hill to beat chargers however there is only 1 fight that you can not use hill that is when you do the quest, however, with enough battle advantage points, you still can use edge of the map to kill those elites.