The number of computational cores is most crucial during final rendering that is why 25% advantage Athlon II X3 435 demonstrates over Pentium E6500 is not surprising at all.
The third core doesn’t matter too much in Mathematica 7 that is why Athlon II X3 435 can only boast taking down Athlon II X4 620, which most likely happened due to significantly higher clock frequency.
Like many other applications, Microsoft Excel belongs to those applications that can distribute the load efficiently over multiple computational cores. But in this case we see a very uncommon result: Athlon II X3 435 is convincingly ahead of dual-core Athlon II X2 250 and Phenom II X2 550, but at the same time loses to its dual-core direct competitor - Pentium E6500.
Adobe Photoshop is also way better optimized for Intel processors. Pentium E6500 outperforms AMD CPUs from the same price range no matter how many cores they’ve got.
Archiving is sensitive to the amount of available cache memory that is why we see Phenom II solutions at the top of the diagram. However, Pentium E6500 also can’t boast a large cache that is why Athlon II X3 435 looks way better compared to it.