Granted KA is more powerful and rare in that it can break an ET and also manipulate the target, but in general Tsukiyomi is better for most practical purposes of battle. If you are a ninja on the frontlines and you had to pick one or the other you go with Tsukiyomi. Tsukiyomi does not require massive recharge times like KA does. It can hospitalize an elite sharingan using kage level ninja like Kakashi in under one second of real time. It does not require maintenance, just a click and shoot.
1st of all KA never "broke" edo tensei, it just took control of Itachi, so the edo tensei user couldn't control him until his job would be done.
Tbh, I have to completely disagree with your overall statement. Tsukuyomi can in no way even compare one bit to KA. KA is by
far much more useful than tsukuyomi.
Now your example is quite slim. A war, a battlefield, the winner is not the one with better jutsu, it is the one with better information. KA is not a battle technique. It is made for espionage. You can take control over an enemy, order him to obtain, whatever information from his village
without being discovered, and make him bring the information to you. Say, if it was used on a highly ranked shinobi, even a kage, it could be of immense usefulness, not only to the owner but to all his allies. Like knowing your enemies strategy for attacking your village. Obtaining such information, can lead to total victory. Then the effects of tsukuyomi in the actual battle is 1 on a 1000 scale compared to KA (being 1000). U_U