You can't really compare CPU's based on their clock speed any more. The Core 2 Duo essentially adds another processor, much like adding a second engine to a car, truck, or tractor. Your top speed doesn't change, but getting from point A to point B will certainly be faster. That is key in computers. The faster speed is really only good for long equations or solutions. Most of what goes on in personal computers is a series of simple short problems.
If you want to compare processor power it is best to see the benchmarks and check the manufacturer's websites.
The HP Media Center is really geared to just that. Media. To fully use its functionality you should hook it to your cable or satellite system. It acts as a PVR or Tivo system to record television for later playback.
The AMD processor might be a little faster. It has a 2.6Ghz speed, but only 2 Megs of L2 cache. The Intel runs at 1.86 but the 4 Meg cache helps make up for the lack of speed. It is just really hard to compare a Intel vs. AMD on paper. Just best to run them.
Out of the two you have listed, I would go with the Intel based one for the office. The only real difference is the High Def TV tuner. If I was buying for home, I would get the AMD version.
Personally, I would go with a Dell Dimension system and customize it for what you are going to use it for. You can get the base E521 which has a faster processor and a 20 flat panel screen for $969. You can look online for coupons that will cut the price as well. Like this site:
http://slickdeals.net/coupons.php?category=tech Right now you will notice a coupon for $300 off their Dimension line that is $999 or higher. If there is a computer just below that price, customize it and add something to bump the price up to $999 or higher.