Oh boy, this is a good one. Strap in. I'll be answering on the basis of the Allied Theater in China.

Short answer: Yes, drama and infighting persisted throughout Allied command structures throughout US-RoC-UK military leadership in China.

Answer in the form of poetry:

I have waited long for vengeance, At last I’ve had my chance. I’ve looked the Peanut in the eye And kicked him in the pants.

The old harpoon was ready With aim and timing true, I sank it to the handle, And stung him through and through.

The little bastard shivered, And lost the power of speech. His face turned green and quivered As he struggled not to screech.

For all my weary battles, For all my hours of woe, At last I've had my innings And laid the Peanut low. I know I've still to suffer, And run a weary race, But oh! the blessed pleasure! I've wrecked the Peanut's face.

-General Joseph Stilwell, US Commander of the China Burma India Theater, fantasizing about brutalizing Generalissimo Chiang Kai-shek, Commander of Allied forces in China.

Long, more substantive answer:

The Allied Theater in East Asia had more leadership struggles primarily due to its unique structure. The China Burma India Theater (CBI) wasn't comparable to, say, the European Theater of Operations because it wasn't administrated under an overall American chain of command. The China Theater was technically under Generalissimo Chiang's purview, whereas Burma was technically under the British India Command. This made long-term coordination and logistics a nightmare and led to regular confusion and miscommunication among lower-ranking officers. Regularly, Allied officers were forced to interpret contradicting orders from British, American, and Chinese high commands. These organizational problems began to exhibit themselves in personality clashes, easily the most famous of which being the Stilwell controversy.

Joseph Stilwell was, by all accounts, a caustic guy to start with. He was famously no-nonsense and straightforward. And he despised Chiang Kai-shek. In his defense, Chiang didn't care for him either, as the Chinese leader viewed him as an arrogant interloper who was far too willing to sacrifice Chinese troops in the field. Chiang's distrust led him to often countermand Stilwell, complicating the CBI and further driving American and Chinese officers at odds.

Stilwell and British officers also clashed as the American began to suspect his British counterparts had no real commitment to Asian operations. To some extent, this was true as the British Army and Navy frequently were forced to abandon supply/troop deployment promises in order to reserve strength for Churchill's "Europe First" strategy.

If you're interested in this vitriolic command climate and the interesting effects it had on US-China relations following the war, I highly recommend Rana Mitter's Forgotten Ally: China's World War II which features an extensive re-examination of the CBI and its issues from a Chinese perspective.