Trotsky was no less dedicated to state terror against "enemies of the revolution" than Stalin. Also, he opposed the NEP all along, whereas Stalin went along with it. (Stalin turned to all-out collectivization only after becoming General Secretary; it gave him a club to wield against the Right Opposition, which was associated with the NEP.)
The difference would have been in their relations with the Party. Here I think it may be useful to contrast Stalin with Hitler. Hitler had genuine personal charisma and oratorical skills. His Nazi henchmen were completely obedient to him; the Nazi rank and file adored him. He "purged" a few rivals and old enemies in 1933, but otherwise counted on (and got) the loyalty of the Party, the army, and the state. (To be sure, the Gestapo was there to suppress dissent; but the Gestapo was far smaller than the Soviet Cheka.) His personal hold on the nation was so strong that the Schwarz Kapelle dared not try to act against him till he had been discredited by the disaster of Stalingrad.
Stalin had no such personal political strengths. He built up power by exploiting his position as Party administrator for several years to fill the apparatus with followers. He eliminated his rivals in the Politburo by playing them against each other. Then when he had secured supreme power, he launched the Great Purge to liquidate anyone who was not completely loyal or had any independent political credit - i.e. the surviving "Old Bolsheviks".
Trotsky would have been more like Hitler. He had IIRC real oratorical skills and didn't feel the need to buy loyalty with favors. Nor did he view anyone with revolutionary credentials as a personal danger.
Therefore, no Great Purge.