Price - price wise, both companies are fairly low, though that could also be that desktops have gone down in price over the years. For the more 'bang for your buck', Dell wins here. Their lowest priced desktop's subtotal came $200 cheaper than HP's and this included a faster processor, more memory, a free monitor, and one year tech support. HP doesn't even offer any of their support free (as Dell does for the one year).
Customization - both Dell and HP allow you to customize your computer the way you want before you purchase it. Everything from the operating system, to the processor, to the graphics card is customizable. However, just like with price, Dell is a bit of a winner here as they have a little more leeway. HP seems a little behind the 8-ball when it comes to the upgrades; a mini laptop at Dell naturally comes with Windows 7, while HP's comes with Windows XP and charges $20 extra to upgrade it. Not to say that there aren't people who still want XP, but with the Virtual XP that comes with the pro version of Windows 7, it would make sense to spend more for that, especially when Microsoft announced they would no longer support XP.
Reliability - this is where users differ; some HP users say their computers last forever, the same is true for Dell users. I've personally seen HP's just fall apart, but I've also seen that with Dells too. However, going with the above, if warranty is what you're after, Dell at least includes a year warranty which is standard on all its systems, with options to go up to 3 years. HP starts their warranty at 2 years at $59.99.
Winner: Undecided/Dell if warranty price