Lin is a far better commander compared to Peng, even in the Red Army period, Lin is a better commander compared to Peng, as for the war with Japan, Lin was injured after that Ping Xingguan, so no further battle for him. Whereas Peng did command the army and fought the Bai Tuan Da Zhan, but whether this campaign was a success or not is questionable, since after the Japanese counter attacked the Chinese lost one of its best aid-de-camp, and Peng himself was nearly captured. During the civil war era, Lin really proved himself to be the god of war, he totally changed the balance of power in mainland China in his 4 years stay at Manchuria. He only had less than one hundred thousand troops to start up with but at the end, his entire army grew to one million men strong with the best equipment in the communist army, and that army like the Manchurian of the old, fought from Heilongjiang all the way to Hainan island. Even Peng’s initial success in Korea was based on Lin’s army, all the army commanders, staff members were in fact worked under Lin during the civil war, they were part of Lin's army. Apart from phobias I think the reason for Lin not to command in Korea is the Mao’s fear of him, Peng is simple and loyal to Mao and would obey Mao’s command, as demonstrated during the 5th campaign in Korea War, he initiated the campaign because Mao wished him to do so, regardless the opinion from the field commanders. If Lin was in command, he would have defied the wish of Mao, just like he had defied Mao’s command during the civil war. Also to note during the cultural revolution Peng was physically attacked by some of the Korea veteran generals simply they hated him for his way of command, the disregard to troop’s life.