Prussia had it's own war ministry and the General Staff in charge of it's army. Bavaria, Saxony, Baden and Wurttemburg also had their own war ministries and staffs, and when war broke out in 1914l, 4 Bavarian, two Saxon, and one corps each from Baden and Wurttemburg were mobilized. Crown Prince Rupprecht of Bavaria's Sixth Army in 1914 was basically the Bavarian Army.

One ramification of this, it could be said, was of increasing the power and position of the General Staff, which operated virtually autonomously from the German state, answerable only to the Kaiser. The German Empire was by far the most militarized state in Europe, as /u/Sid_Burn notes in this excellent answer [here] (https://www.reddit.com/r/AskHistorians/comments/2eo2u8/why_is_ww1era_germany_seen_as_a_highly/ck1fick), and the increase in the Germany Army's size and prestige as a result of unification certainly had far reaching affects on Germany and Europe, especially with regards to Kaiser Wilhelm and World War One.

I heard of one particular instance in which a Bavarian General refused to fight on a particular front for example during WW1 however I don't have any idea of the validity of this claim.