The Swiss Halberdiers are better than the Billmen as they're more powerful and no one can get an armor bonus when attacking them. If you can get billman to valor 1, gold sword, and gold shield, you have a unit of Chivalric Footknights. Then there's JHI which makes even Chivalric Knights evaporate like peasants.

The only better infantry(1 v 1) in the game are Gothic Foot Knights(try 2 JHI vs 3 GFK and you'll see). Gothic Foot Knights have giant Armor Piercing Swords making them the best swordsman in the brute force stat wise.

Byzantine Infantry is still my favorite swordsman. You have to love these guys unless they mass rout on you and you have to take a 20 stack with your 14 star Jedi General. They're the only swordsman unit that can take cavalry out since they outnumber them 2-3 times. Just get them moral and attack upgrades and they'll be good throughout the ages.