From a reading of Evan Mawdsley's *The Russian Civil War* it is not clear to me that Wrangel would have done any better than Denikin:
"As regards Denikin's strategy in the south, two distinct and partly contradictory criticisms have been made: first, that he advanced in too many directions; and second, that he moved too quickly. The Moscow Directive of early July both set a daring objective *and* proposed an advance by widely spread armies. Baron Vrangel, Denikin's successor and one of his main critics, called the Moscow Directive "the death sentence of the South Russian armies" and stressed the dispersal of effort: "Striving for space, we endlessly stretched ourselves into a spider's web, and wanting to hold on to everything and to be everywhere strong we were everywhere weak." Denikin defended the spread and pace of his attack by saying that the normal laws of strategy did not apply to civil war. "We lengthened the front by hundreds of versts and became from this not weaker, but stronger." In south Russia the offensive took grain, military supplies, and manpower from the Reds and gave them to the Whites. At the time even Trotsky saw the situation much as Denikin did: on the Donets and in the Ukraine, "we left Denikin complete freedom of action, and gave him the chance to obtain a huge reservoir of new formations."18
"Vrangel had a counterplan. In July he questioned the order to march his Caucasus Army north through the Volga region. Instead, the bulk of Caucasus Army, "a major cavalry mass of three or four corps," should be transferred to Kharkov, between Don Army and Volunteer Army. This concentration in the center of the AFSR front might just have brought Moscow's capture. (Denikin's response, according to Vrangel, was "Aha, you want to be first in Moscow.") Kakurin, the Soviet military historian, felt this to have been the best plan, and Lehovich, Denikin's biographer, saw it as the point where history might have been changed. Denikin himself, however, later claimed that he rejected Vrangel's plan because Tsaritsyn had to be held to protect Rostov, and it is hard to see how such a transfer could have been effected in the face of Shorin's August offensive.19 In addition, shifting a large force 400 miles from Tsaritsyn to Kharkov would have been difficult. Vrangel's July 1919 proposal shows that he at least could not fairly make the other main criticism of AFSR strategy-—that Denikin moved too quickly; the involvement of Vrangel's cavalry would have led to an even more precipitate lunge. "To Moscow!" became the motto of the southern Whites from July, and the September—October advance on the Soviet capital ended in disaster. But in Moscow Denikin did find a goal, both symbolic and concrete, for his troops. Certainly this was what the army wanted; Denikin admitted that he had been optimistic in July, but so had the whole army leadership—"the Cassandras were silent." The rapid occupation of territory kept a larger enemy army off balance. "Our strength," Denikin recalled, "lay in the upsurge (*pod'em*) brought about by victory, in maneuver, and in the momentum of the advance."
"Denikin made several important misjudgments. He did not realize how poorly consolidated his rear was, and he saw Soviet power as unpopular and unstable, ready to break under pressure. But had he (correctly) assumed effective Bolshevik consolidation he would have been even more justified in attacking, because time was not on his side; every passing week let the Reds shift more combat veterans from the Siberian front and raise fresh formations from their huge territory. The Moscow offensive failed, but that does not mean that another strategy would have succeeded. The Red Army historian Kakurin believed that Denikin's best chance would have been the earliest possible attack on Moscow..."
https://books.google.com/books?id=yBDFwj6Ya1wC&pg=PT294
Mawdsley also notes the supply problem which I can't see either Denikin or Wrangel solving:
"The rear of the AFSR, however, was its real military Achilles heel. Even the best organized army, had it been in the AFSR's position, would have had trouble with its supplies. In October 1919 the leading White units were 400 miles north , the nearest supply port (Taganrog), and 600 miles from their bases in the Kuban. The railways suffered from neglect and war damage, and the fleeing Reds had taken rnuch of the rolling stock with them. But on top of this the AFSR supply organization, and the rear in general, were in a very poor state. Vrangel in December 1919 gave two reasons for White failure, faulty strategy and "the absolute disorder of our rear. The British Mission complained of .an entire absence of what we understand by good q[uartermaster] work and administrative efficiency.23
"Administrative inefficiency and poor supply lines made the advancing whites rely on *samnosnabzhenie* (self-supply). The requisitioning of supplies from the local people often degenerated into looting, with extra booty being shipped to rear bases (further disrupting the railways). "Self-supply was used to reward success, as Mai-Maevsky told Vrangel: "If you demand of officers and soldiers that they be ascetics, then they won't fight." ("Your Excellency, in such a case what would be difference between us and the Bolsheviks, asked Vrangel. "Well," came the reply, "the Bolsheviks *are* winning." "Self-supply" led the Volunteer Army (known by its Russian abbreviation as Dobrarmiia) to be nicknamed "Grab'armila" or "Looter Army" by its victims. In September Denikin wrote to Mai-Maevsky that he had learned from his supply officers of .this gloomy picture of grandiose looting and plunder, the bacchanalia of arbitrary rule, which reigns unchecked in the whole front-line zone.". 24 Denikin, then, was aware of the problem, and its bad impact on public opinion and the troops themselves, but he could apparently do nothing about it."
https://books.google.com/books?id=yBDFwj6Ya1wC&pg=PT297
