I give my preference to AMD Athlon X2 Dual Core because these are very affordable, and supposedly efficient.
And here we have the fanboys at it again. Athlon II X2 will definitely give you more bang for your buck, but Intel Core 2 Duo will outperform it in certain cases.
Core 2 is the faster chip. The Athlon X2 can outperform the Core 2 for 64-bit, but that's about it. Even the 6400+ has issues competing with mid-range Core 2s. At this point, you might as well get an i5 or Phenom.
I haven't exactly been up to the latest fashion, but generally Intel is better, AMD cheaper, and on rarely few occasions a bit better. In most cases Intel dominates flat out. The thing about AMD is, it is cheaper, but at the same time consumes a lot of energy, which A: means it costs more in keeping. B: You won't be getting as much software integration. Why B? because integration takes cross platforms, and with a hungry power drain, you will have a lot less mobiles and tabs specified to work with AMD. And this is where the trend of computing is leading towards. So, even if at first going to Intel feels like going to the enemy, it's generally better.