Army wise, Seika is better overall.
Kanmei > Sleepbashou extreme diff I think everybody can agree with this.
I know everybody including me shits on Jigaga too much (unlike one certain individual who twerks when he kicked the bucket), but martially, he should be strong enough to beat Rinbukun. I rate Jiaga on par with Gyou'Un, Bananji, Akou, and Kaishibou.
But Kouyoku and Hakurei can't beat Kansaro and Gakushou in warfare despite Yoku is the strongest one here martially.
So it's up for Kanmei to defeat Shiba before the Chu gets to him. I believe Kanmei can defeat SBS before the rest of Seika generals get to them but Kanmei will get killed by the rest. So Seika wins.
Add Jokekaryuu in and Seika washes.