I studied Russian history more than 15 years ago, so this may all be outdated, but what I learned then was:

• Personally, they were very different. Trotsky was Jewish intelligentsia: cosmopolitan, sophisticated, an accomplished literary critic as well as revolutionary, and something of a snob. Stalin was the son of a poor village tradesman, educated at the seminary, known mostly for his skills at bank robbery. Among the Bolsheviks, Stalin was considered a dimwitted drone, someone who'd do the paperwork but not someone who could ever run the country---that's why Zinoviev and Kamenev were so willing to bring him into the "troika" that ran the country after Lenin's death; they thought he could never be a threat. Trotsky was known as an intellectual, and made sure everyone knew it.

• Ideologically, they had very different ideas of the future of the USSR. Trotsky wanted world revolution, a foreign policy based on fomenting communist revolutions in as many nations as possible at all times. Stalin believed in "revolution in one country", consolidating the domination of the Soviets in Russia and Ukraine rather than making enemies all over the world. WWII just happened to drop lots of territories into his lap, and he was never one to miss an opportunity.

• On an entirely personal note: Stalin had a thick Georgian accent, which marked him as something of a hick. Trotsky spoke very eloquent literary Russian, and he allegedly made fun of Stalin's manner of speaking. This did not endear him to the notoriously sensitive Stalin, who had been a published (terrible) poet before he got into politics.