I see three possible factors:
1. 3% should be noticeable.
2. Larger ring/cog on the new set-up should lead to a small reduction in chain friction that might not be noticeable but for the 3%.
3. It should be both cleaner shifting and a smaller jump to drop from your middle ring to your new small chain ring. This may allow you to keep more momentum as the hill picks up, which shortens the hill.