We might make a few comparisons between Generals Wavell and Auchinleck. Some obvious things to examine are appointments and their strengths and weaknesses.
Based on results, General Wavell seems to have done well with his appointments. He was in his position for about two years. Auchinleck held his position for only about a year. General Auchinleck did not do well with his appointments, and I have wondered at the difference. One example was Alan Cunningham, who had done well in East Africa, and had conducted a fast-moving campaign that routed the Italians. The problem was that General Cunningham was near exhaustion at the end of the campaign. General Auchinleck was more impressed by Cunningham's campaign, and seems not to have been able to assess the man.
Wavell's primary strength seems to have been his planning ability. His ability to judge men was another strength. His weaknesses were his verbal inarticulateness and his seeming inability to recognize which orders from Britain were reasonable and which were not. He accepted the end to the offensive in Libya without protest and the adventure in Greece. Both turned out badly. He objected to Iraq and Syria, both of which turned out well.
I have wondered if General Auchinleck was more of an idea man. One factor that I had not considered was the Auchinleck was an Indian army man, and lacked much exposure to the regular British army. He did not do well with his appointments, but he proved himself a brilliant field commander, something that was not consistent with his position as theater commander. Auchinleck saved the Crusader battle, in late 1941, and turned it from a defeat into a victory. He then turned the 8th Army over to General Ritchie, who was not up to the job. Auchinleck had to step in and restore the situation, finally halting Rommel at the First Battle of El Alamein. He and his chief of staff, Eric Dorman-Smith, were removed by Churchill, as Churchill had finally lost confidence, and politically, needed to make a change.