Here's a clause-by-clause comparison of the two Constitutions. There weren't many changes at all; most of the few present were restrictions on federal spending. The central government couldn't spend money on internal improvements; they couldn't pay money without a specific dollar figure voted on by Congress; they couldn't make up earmarks in Congress; they couldn't dump spending into omnibus bills. All of these abolished practices the South had objected to in the antebellum period.
There were a couple reforms to the executive too: the President served a single six-year term, and the cabinet officials could speak (but not vote) in Congress should Congress allow it. Finally, the President also had a line-item veto.
And finally, they specified they were forming "a permanent federal government." Did that mean no state could secede from the Confederacy? They didn't specify.