This is a contentious issue, as many issues related to the USSR are given the inexorable political climate surrounding the history. There are two dominant narratives.

One narrative views Trotsky sympathetically, and is shared somewhat oddly by Trotskyists, some anti-communist leftists, and many Western liberals who had some sympathy with the revolution in Russia, but disliked the state that emerged under Stalin. This is a somewhat familiar narrative - Trotsky was perhaps not a great guy, but he was better and more competent than Stalin. Trotsky himself was pretty dismissive of Stalin as an intellect. However, through political machinations and manipulation and terror, Stalin managed to ostracize Trotsky and eventually chase him out of the country where he traveled far and wide before succumbing to Stalin's hand in 1940.

Another narrative focuses on the question of why Trotsky was unpopular in the Party in the 1920s and what precipitated his exile. Why, for example, was Trotsky such an object of fear among the Party elite in the 1930s, but Bukharin - also an opponent of the Stalin-bloc's policies in the 1920s - remained legitimate until the haphazard circumstances surrounding his arrest and eventual execution in 1937-38? This portion of the narrative seems crucial to me. Ideologically, Trotsky and his bloc advocated a number of policies in the 1920s that were seen by the Party majority as reckless and dangerous, politically and otherwise. He advocated for collectivization and super-industrialization when the majority of the Party- including Stalin, incidentally - favored the NEP as a development model. He also advocated a form of international socialist revolution, and denied the prospect of socialist economic development without the aid of foreign socialisms. After the Civil War, and the associated political chaos in the countryside, it is understandable that many Party secretaries viewed a renewed offensive against the peasantry as politically problematic or even suicidal. Trotsky and his so-called 'left opposition'ists also tended to advocate for greater worker democracy to challenge the Party secretaries. To my mind, this is probably similar to Stalin's effort to stimulate greater democracy to discipline Party secretaries in 1936 rather than a genuine ideological commitment to democracy. Trotsky himself showed rather resourceful at developing means of crushing democracy during the Civil War when it appeared that the revolution was under siege. Are we so sure he would not do the same as the predominant political figure in the early USSR?

Regardless, the combination of these policies made Trotsky unpopular, and when he was essentially marginalized as a political figure, he helped to organize protests in the streets and public opposition to the Party. This is ultimately his greatest crime in the eyes of the Party elite. The Bolsheviks were organized along the principles of something called 'democratic centralism,' which holds that Party deliberations may, internally, be extremely democratic and contentious, but once a decision is made, the Party must show a unified face to the public. Trotsky circumvented the Party majority to stimulate opposition in the streets and for this he was essentially chased out of the country. Notably, many of the other left-oppositionists made amends with the majority and moved on. It's easy to look back from the standpoint of 1940 with Trotsky, Zinoviev, Kamenev, Preobrazhensky, Muralov, Radek, etc. having been arrested and killed or otherwise eliminated to conclude that the Stalin elite never got over the opposition of the 1920s but this is mistaking subsequent contingent events as being embedded necessarily in earlier ones. In 1930, the industrialization advocated by the left-opposition had only just begun, the leadership cult around Stalin did not really exist, and the left opposition outside of Trotsky were reintegrated into the Party. It was only due to subsequent events that Stalin and his cohorts (perhaps more his cohorts than him - though this is debatable) renewed suspicion about the loyalties of these former opponents.

So ultimately your question - how much truth is there to the Trotsky is good narrative? This is actually a very difficult question. I personally don't view Trotsky as particularly distinctive from other Bolsheviks, but I also put less emphasis on the individual of Stalin as the sole creator or generator of the terror of the 1930s. I think given similar conditions - which, incidentally, Trotsky advocated (as well as a more aggressive foreign policy) - it is plausible that a Trotskyist leadership facing peasant resistance would also authorize repression of rural opponents. Further, given that I am unconvinced by claims that the central party apparatus orchestrated a famine - rather, the evidence in my view shows the famine as a crisis of significant proportions unforeseen by the central leaders - I am further skeptical that a Trotskyist leadership would have prevented some of the worst tragedies of the decade. It is just an easier narrative to say that Stalin was the Big Bad, and Trotsky was the martyred true king defeated only through deception and intrigue by the usurper.

As Vladmir Lenin succumbed to sickness and the end of his leadership drew near, several candidates to succeed him arose. Leon Trotsky, leader and founder of the victorious Red Army, was an obvious choice. Too obvious, perhaps, for his own good. His competition, most notably Stalin, worked to defame his name, drawing on alleged conflicts with Lenin and attempts to credit himself more than the Bolsheviks. They were successful, and Trotsky slowly fell from power, first losing his Red Army position and then his government seat. By 1929 he was officially expelled from the Soviet Union. He spent the rest of his life in Turkey, France, and Mexico, where he was assassinated in 1940 under Stalin's orders. During this exile, Trotsky composed his most known work on the USSR, The Revolution Betrayed. It's certainly a must read if you have any interest on the subject, though it can get a bit dense and statistical. The book points out a myriad of flaws in the Stalinist Soviet government, and predicts the eventual downfall of the USSR by revolution or state-supported capitalism. If you're a capitalist Westerner looking for mud to sling at the Soviets, what better source is there than from the very man who led the revolutionary army? They're so messed up over there that even the guy who started the whole thing thinks it's gone down the drain. I cannot say anything about contemporary views; Trotsky worked with American socialists in Mexico and continued to support a better-functioning global Communism movement, so he may not have had such a great rep after WWII. As the leader of a rebel military force, he also was likely involved in activities not befitting of the "good guy" title, though exact details on his actions were twisted by political opposition. The modern "good guy" view thus derives more from "the enemy of my enemy is my friend" mentality.

TL;DR: Since he led a rebel army, he probably did some bad stuff. But he was also exiled and by Stalin and wrote about how crappy the USSR had turned out, even though he put so much work into starting it, so that made him okay in a lot of people's books.