Could you be a bit more specific about this question and what characteristics you're referring to? I'm not sure if there's a meaningful way to answer your question at the moment. Yuan Shao, while a key player, isn't exactly a terribly colorful character, and the broad strokes of the portrayal of him is correct. He was a member of the powerful Yuan clan and a key figure in the events in Luoyang that led to Dong Zhuo's rise to power, but would end up leading the coalition against him. After Zhuo's death, Yuan Shao remained one of the most powerful warlords in China (together with Cao Cao and Yuan Shu) thanks to owning vast tracts of very wealthy land and familial prestige. He eventually lost the war against Cao Cao (the show streamlines the war a fair bit) and, well, died.

It's been a while since I watched the 2010 show, but the most prominent personal characteristics of Yuan Shao I can remember it showing are indecisiveness in the face of conflicting advice and a tendency to ignore the highly useful suggestions of Xu You. Is that what you're referring to?

Not seen the show but I can comment on Yuan Shao's personality.

On the four traits brought up in the discussion, he was accused of being indecisive, he ignored Xu You possible twice but not constantly but is often accused of failing to listen to the "right" advice at Guandu (Ju Shou and Tian Feng most notably) and about taking in the Han Emperor (though he did listen to the right advice on other occasions). Arrogance is one of the charges but may be overegged, foolish would be harsh.

Personality and abilities

Yuan Shao was handsome who carried an air of authority even from his youth, he gathered many around him (not hurt by family prestige or being the wealthiest family in the capital), an expert networker. He was a rich young man about town who strongly disliked the eunuchs, despite their role in the family wealth, helping He Yong organize escape lines for eunuch opponents. As an officer of He Jin, he was a major figure in pushing for He Jin to act against the eunuchs and for bringing in outside forces. This was not good for the Han or He Jin and Yuan Shao is accused of forging orders to local authorities, after He Jin was killed Yuan Shao would slaughter thousands as the palace burned. Having failed to move against Dong Zhuo in the immediate aftermath, he fled soon after the coalition would soon begin.

If Yuan Shao's role against the eunuchs has become more heroic despite his mistakes and bloodthirsty advice then his actions, his role in the coalition is perhaps viewed more harshly than it should. Was made its chief due to family position, he is accused of arrogance and of being petty during it to men like Zhang Miao, he couldn't keep other more powerful figures under control, but his blockade strategy was effective and arguably the best path forward given the troop quality and experience disparity when facing Dong Zhuo.

As a warlord, he did go from one city Bohai relying completely on supplies from Han Fu to a powerful figure in the north, controlling two provinces and with some degree of control in another two. His name and prestige certainly helped, his connections from his days at the capital would bring him officers but it wasn't just that. Yuan Shao implemented Peng Ji's plan perfectly to take Ji by bluff, he won the support of men like Qu Yi and Ju Shou and promoted them quickly. His defeat of the experienced Gongsun Zan close to Ji Bridge was an upset and he was an able but slow commander, breaking the power of the Black Mountain Bandits with his long march (with Lu Bu) through the mountains, he took back Dongjun from Zang Hong, over many years with help from likes of Yuan Tan and Qu Yi, he destroyed Gongsun Zan.

However all these took time and it took him years to destroy Gongsun Zan, allowing Cao Cao to strengthen his position, he lacked the ability or willingness to fight on two fronts. As a commander, he was inferior to Cao Cao which is no shame but a bit of a problem when facing Cao Cao. He does not seem to have developed the administrative strength that Cao Cao did to support his armies and his lands and there were concerns in his camp his armies were exhausted. His use of family members to govern his lands was nepotistic, he may have trusted them and sought to test them with varying success but it didn't ensure the best was got out of his lands.

As a political player, he built alliances that dominated the early parts of the civil war and would come out on top over Yuan Shu, his patronage and support were important for Cao Cao's rise. He knew the value of propaganda and used Chen Lin well, he was able to outmanoeuvre Cao Cao in the political arena when Cao Cao first got the Emperor though, by Guandu, Cao Cao had firmly outmanoeuvred him with Yuan Shao unable to raise support from other warlords. Yuan Shao does seem to have failed to initially realize the danger if someone else got control of Emperor Xian in 196 while his failure to make a clear decision on his choice of the heir was a complete disaster that doomed his family.

As a man, he was calm under pressure and did show bravery at times, a man able to inspire loyalty and popularity from those around him though by the end he was not able to command unity with his camp dreadfully split. He could be violent as the eunuchs discovered and attempted to assassinate both Lu Bu and (via Cao Cao) Zhang Miao among others, he treated those of station generously but is accused (not without some cause) of being suspicious, of being arrogant (again not entirely without some cause), of being leniant with the mighty and unable to impose order, of being indecisive which might explain the slow conquests. It can be a little unclear if some of the charges like weak governance are true, exaggerated or simply made up for the compare and contrast.

Yuan Shao reputation and portrayals

Yuan Shao is, in many ways, defined by Guandu. The defeat shapes his reputation and it was iconic for Cao Cao, subject to much Wei propaganda. The number divide gets inflated considerably as Pei Songzhi and Rafe De Crespigny point out, the battle traditionally shows Cao Cao's superiority as a leader but also emphasis Yuan Shao's failings: a camp riven by chaos and infighting, listening to wrong people, treating good men poorly, lacking flexibility, missing opportunities, arrogance. The truth of defeat was rather more complicated and he may even have been entering the war on the back foot rather than the overbearing arrogant power who then blew it.

The Yuan Shao is an arrogant fool is also built up in other ways, the Yuan and Cao dynamic gets twisted so Yuan Shao's political humiliation of Cao Cao when Cao Cao charged him with faction (a most serious charge) is turned into modest Cao Cao appeasing Yuan Shao's arrogance, Yuan help in the early days both politically and militarily is played down. Other factions future Wei officers speak wonders upon Cao Cao's superiority in the build-up to Guandu and we have famed speeches from Guo Jia and Xun Yu, ten points of how Cao Cao is better than Yuan Shao to lift Cao Cao's spirits, that may or may not be entirely accurate recordings of what was said but represent the message Wei was sending. Xun Yu's (translation Yang Zhengyuan) speech

Considering the successes and failures of ancient times, those who truly had ability, though they were weak they were certain to become strong, but those who did not, though they were strong they became weak. Liú [Bāng] and Xiàng [Yǔ] in their successes and defeats are enough to demonstrate this. Now the only one who can contest the realm with you is Yuán Shào. [Yuán] Shào appears outwardly lenient but inwardly is jealous, appoints people but suspects their intentions. You are of wise judgment and adaptable, and only ability determines appropriate [appointment]. This is superiority in judgment. [Yuán] Shào is hesitant and makes few decisions, missing opportunities. You are able to decide great affairs, and adapt to changes without limit. This is superiority in planning. [Yuán] Shào’s military discipline is lax, his orders are not firm, and though the soldiers are many, infact they are difficult to use. Your orders are clear, rewards and punishments are enforced, and though the soldiers are few, they all fight to the death. This is superiority in military. [Yuán] Shào relies on his family accumulations, feigns appearances of wisdom in order to collect famous followers, and therefore many gentlemen of little ability but good reputation follow him. You use benevolence to care for people, sponsor sincerity and not empty good appearance, in your own conduct are solemn and frugal, but in rewarding the accomplished begrudge nothing, and therefore the truly loyal and upright gentlemen of the realm all wished to serve. This is superiority in virtue. With these four superiorities to support Heaven’s Son, wielding justice to go on campaign, who dares be disobedient? What can [Yuán] Shào’s powerful words do?

Their arguments are skilled rhetorical devices that show Cao Cao as superior to Yuan Shao in ways of leadership and character while helping build the image Wei wished to send about Cao Cao. Yuan Shao was a famed leader but inferior to Cao Cao, our brilliant founding leader.

An image has built upon that: Cao Cao is the brilliant man of the new age, Yuan Shao a representative of a faded old guard who can not handle the change and rely on their name. The novel runs with that theme, emphasizing Yuan name and arrogance even further, modern adaptations can go even further. Yuan Shao's successes before Guandu can get overlooked or, when touched upon, underplayed so people's focus is on his worst moment as a warlord.