Intel for sheer computing power. AMD for VFM.
Even in the past when AMD was faster and cheaper, many users chose Intel simply because Intel was the more prominent brand; that is, they'd seen and heard more of Intel.
Since the introduction of Core 2, Intel took the lead in raw power, but is generally more expensive. As others have said, the choice depends on your budget constraints and performance target.
For example, compare the Intel i7 920 and AMD Phenom II X4 920. Broadly speaking, the Intel 920 is faster by about 20%, but costs several thousand rupees more. Moreover, a matching motherboard based on the X58 chipset is still quite expensive and uses the faster but more expensive DDR3 RAM. The total difference in system price can be quite high.
Personally speaking, since I'm neither a rich hard-core gamer nor a video editing professional, it doesn't make sense for me to spend that extra 10-20k to gain a few fps in gaming or a couple of minutes while rendering a large movie file. I consider the money better spent on a gfx card, more RAM, hard disk, external storage, etc. etc.
But that's just me. Others will have their own priorities and values.