The battle for Burma was wasteful in terms of resources for both sides, and quite frankly, the same challenges that Japan faced when invading Burma from the East the UK faced when trying to push back East. I would label it as more of an ancillary action focused primarily to prevent Japanese incursions into India. In most ways, this was an extension of Japan's invasion of China in that its main goal was cutting off China from Allied resupply and reinforcement. The importance of the Island Hopping campaign was that it slowly bled the Japanese fleet dry of ships, sailors, and naval aviation assets. Most historical analysis of the Japanese strategy during the Second World War is, plainly, that it was divided. Both the Army and the Navy had very different goals. The Army wanted to focus on subjugating China, while the Navy was concerned with establishing a protective buffer around the Home Islands, as well as the extremely important resources supplies that the East-Indes could provide.

The Burma Campaign then was a factor (albeit a somewhat small one) in the defeat of the former, while the Island Hopping Campaign was a defeat of the later. Which was more important? Well, the Army was bled dry in trying to take and hold China, while the Navy was bled dry trying to take and hold the Pacific. So both were pretty bad news for Japan. That said, as an Island nation, most military historians would likely point to the loss of her fleets as a more crushing blow. Without them, she was a sitting duck for a land invasion and could not reinforce and resupply her armed forces in China or on remaining Island redoubts. In any case, if one considers the Island Hopping Campaign more definitive in its impact than the land war in SE Asia, it is not by losing Islands like Okinawa, but rather, the cost in ships from the naval battles in defending those islands (and previously, attacking) that was the most imperative part of that campaign.

A good primer on this would be Costello's Pacific War, and for more information on Japan's strategic thinking (and lack of cooperation between branches) check out James Wood's easy to read Japanese Military Strategy in the Pacific War.

There's still some doubt among commentators whether China contributed to Japan's defeat. For example, Max Hastings writes in his popular history of the war Inferno that China "was incapable of participating effectively in the war. China was merely a great victim, second only to Russia in the scale of its suffering and losses, and was denied the consolation of any redemptive military achievement." This does a great disservice to the Chinese, in my opinion. Fortunately, their sacrifices and achievements have started to receive greater attention from scholars, especially in the last two decades.

Despite misgivings about the competency of Chinese Nationalist leadership, the United States and United Kingdom continued to support Chiang Kai-shek's regime until the end of the conflict for a very practical reason: the bulk of the Japanese army was committed in China. Both Roosevelt and Churchill worried (perhaps rightly) that, if China were to go under, Japan would redeploy its forces in the Pacific or mount large-scale operations against India. Moreover, the war with China drained Japan's resources; indeed, that's the original reason why Japanese leadership decided to expand into the greater Pacific and risk a prolonged conflict with the United States.

Some have also argued that China's refusal to capitulate completely undermined the credibility of Japanese propaganda, which justified imperialism on the pretext of Pan-Asianism and creating an "Asia for Asians." In fact, the American Joint Intelligence Committee concluded in 1944 (employing the rather racist language of the time) that "the significance of Asiatics [=the Chinese] resisting the encroachments of other Asiatics is of tremendous political and psychological importance."

I'm about to board a plane, so this overview will have to remain short. In the meantime, I recommend Rana Mitter's Forgotten Ally: China's World War II, 1937-1945 as a decent and affordable introduction to the Second Sino-Japanese War. I hope you find this helpful! :D