Does the new battery last longer, or is it the laptop itself?

That's a good question.

Ifixit does indicate that the 2010 13" MacBook uses a battery with the same dimensions and part number as the 2009 model but with only a 350 mAH greater charge (and it's 7.5 grams heavier): MacBook Unibody Model A1342 Mid 2010 Teardown

The increased battery life, therefore, is due to the 2010 model's CPU, GPU, chipset combination. All things being equal, increasing the battery capacity by 350 mAH alone would net only about 30 minutes longer life in the old model if you were already getting the rated 7 hours.

Just for reference, another hardware change (perhaps the only other substantial one), is that the 2010 version's Mini DisplayPort provides audio out while the 2009 model does not.