Probably worse. Indeed, Trotsky being in power and advocating world revolution could result in more fear and thus more support for Hitler in the West.
More like how Germany did under Hitler; on the warpath after a period time of which would serve as a buildup of military strength to accomplish the goal of spreading the "revolution". In other words, a coming disaster for not only the USSR of which have its economy wrecked but to the world that would be facing the red menace.
As much as I hate Stalin and communism entirely, I often remind myself in discussions like these that we ought to be somewhat pleased that Trotsky never got to rule the USSR.
People keep saying things like this. Have either of you actually read what Trotsky wrote or looked closely at his actions though?
From what I've read, I very much doubt that Trotsky would act at all in this sort of way.
Why?
1) Any leader of the Soviet Union has, as their first priority, the defense of the cradle of the revolution. The Bolsheviks were not raving loonies, but intelligent people whose deep belief in their cause made them willing to make sacrifices and accept compromises
in the interests of furthering their cause. People forget that even Stalin was a true believer in Marxist-Leninism. Willfully gambling with the only successful worker's state when the Bolsheviks knew their opponents were clever, determined and well-resourced was not something even Trotsky was going to do. I am not aware of a single Bolshevik leader who didn't believe that the Capitalists wouldn't unite and crush the Soviet state if they were provoked.
2) In a sense, Trotsky's belief in world revolution made him less militaristic than Stalin. The failure of the revolution to take hold outside Russia and Mongolia did not discourage Trotsky as deeply as it discouraged Stalin. Trotsky had much more faith in the ability of the workers in the capitalist countries to throw off their own chains, without Soviet bayonets to "protect" against counter-revolution.
3) Trotsky was more of an internationalist - that extended beyond his faith in the workers of other countries - it also meant he believed more in keeping the Soviet Union open to trade and travel. That would be of enormous help to Soviet diplomacy and the Soviet sciences (which were deeply damaged by the Stalinist travel bans).
4) Trotsky was too abrasive to wield power in the way Stalin could. Other Bolshevik leaders might accept Trotsky as a weak "first among equals" leader if Lenin had really thrown his weight behind Trotsky (almost certainly this requires Lenin to be healthier and live longer and for Trotsky and Lenin to have a better relationship for Lenin's last years). As such, Trotsky backing any provocative foreign policy moves would provoke a strong reaction from people who didn't like him much and who he was temperamentally incapable of eliminating in the cold-blooded way Stalin operated.
5) Trotsky put more faith in democratic institutions than Stalin (indeed, strong worker/soldier Soviets are probably necessary for Trotsky to gain power, since they are the only likely power base that he could gain that he could and would use - his belief in the Soviets meant they reciprocated by believing in him, and unlike the army, they have legitimacy in the Bolshevik system). I have difficulty for a strong Soviet democracy being keen on exporting revolution when they are still feeling the wounds of WW1 and the Civil War so deeply and when many members of the Soviets, like Trotsky, will believe that Marxist revolutions will occur naturally in their own time and that the main job of the Soviet Union is to survive and prosper so it is in position to aid those revolutions when they arrive.
In a world where Leon Trotsky reads out Lenin's will and testament, which recommended against Stalin being named Lenin's successor, to the 12th Party Congress in 1923 and as a result, becomes the leader of the Soviet Union, how would the Soviet Union as a whole have fared under Trotsky's leadership?
As David T says, this PoD isn't enough to get Trotsky into the top job. You need a better Trotsky-Lenin relationship, probably a longer lived Lenin and probably more hands in the workers and soldiers Soviets when Lenin dies and the succession struggle breaks out.
What would Trotsky look like if he did gain power?
He'd be a weaker leader (not necessarily a bad thing) than Stalin, there'd be no cult of personality, there'd be more debate within the Party, likely that means Moscow is less able to keep foreign Communist Parties on such a tight leash, Soviet science would do better, trade with the West would be more, Collectivization would happen as soon as possible (which may mean no Holodomor, since the massive deaths were a result of Collectivization happening just as drought was ravaging the country) and the NEP would be ended as soon as possible (also probably a good thing, while centralized planning was bad for the Soviets in the long run, it was the most effective path to getting the Soviets ready to resist the German invasion). Almost certainly there is less in the way of purges and while the Bolsheviks were always going to become more conservative during the late 1920s (most of the very liberal reforms rolled back during the Stalinist years were seen by most Bolsheviks as having gone too far even before Stalin consolidated power due to the way they aggravated the ordinary people of the Soviet Union), likely they don't become as conservative as they did under Stalin. Likely, there isn't such persecution of people on the basis of nationality and the smothering of non-Russian culture is largely avoided.
Also, I don't think Trotsky would last in the top job anywhere near as long as Stalin did.
So hardly a rose garden, but I think generally a better Soviet Union for the people inside it and for the neighbours.
But again, it is very, very difficult to get Trotsky into the top job. Zinoviev is a far more likely successor to Lenin.
fasquardon