Either is a good choice if you want to limit the number of hotbars you keep visible at any one time. It is pretty easy to simplify gear so that there is almost no need for hot switches. And, it is relatively easy to simplify combat techniques as well.
Warforged barbarian has the bonus of not becoming fatigued following a rage so you can avoid cool-downs or lesser restore potions.
With barbarian you have only the standard 7 feats to work with meaning you need to be more careful about combat techniques. Is it stunning blow and great cleave? If so, what is needed for pre-reqs? Do you have feats left for the THF line and toughness?
With fighter you get bonus feats so end up with an abundance of options. Of course, all those combat techniques need to be on the hotbar someplace so that you can trip, cleave, sunder, stunning blow, great cleave....
You also need to think about the weapon choice if going Kensai. Falchion does more damage in the non-autocrit calculations due to the bigger crit range. Great axe does more damage in the autocrit calculations due to the bigger multiplier. Which represents the end game you will play?
If you will run epic with characters using mass holds and stuns then go great axe. If not then you should go falchion. And, don't forget that with either barbarian or fighter you are limited as a THF build to blunt or slashing -- there is no two-handed piercing option (unless you want to go for ranged weapons).
Build philosophy is pretty simple with either. All STR and CON. Be sure to have a healer around because you won't have any AC worth talking about.![]()