I've tried both with my Team. The one we found to make more sense is to adjust the estimate. The whole idea of Agile is to update your plan based on new information. Updating your estimates to reflect the work _remaining_ for your Stories will make estimation much easier, and will better reflect what is actually happening in Sprint 2.
The only thing you've really 'lost' is the overall effort that was required for that Story, but it was decided (in our case) that we didn't really even need that.