Those are both excellent choices (though I didn't study your specs in detail). Although, as with any new PC, make sure that, before you try to install any programs on it, you go to the Dell or HP site, then to Windows Update and ensure you have all of the latest updates. (New computers can be months out of date.) And ensure that you have the latest version of Quicktime.
And don't forget about your operating system! Windows 7 64-bit seems to have some challenges with Premiere Elements 8 -- but it's also the future of computing. It's up to you then if you want to go with the 64-bit version and hope things work out or play it safe and stick with Windows 32-bit. In fact, you may want to test drive the program on your new computer before you actually purchase it.
Meantime, don't forget that your computer is only one link in the chain, when it comes to video production. You'll also want to ensure you're using the program with a camcorder that provides compatible video. A miniDV or HDV tape-based camcorder is the absolute best choice. If you've got lots of power (as you will with these machines) you could also edit AVCHD.
One deciding factor is the "flavor" of HD, that one wishes to edit. If it happens to be AVCHD, then the i7 will be necessary. If it's other forms of HD material, then one could get by with less CPU power, though more will not be wasted.
One of the most important aspects of a computer, when editing HD material, is the I/O sub-system, i.e. the HDD's, how they are set up and allocated. Three physical HDD's is about the minimum. With HD footage, performance will be greatly enhanced, if the "media" disk is a RAID, at least 0. While this can be managed from an on-board RAID controller, performance will benefit from the use of a dedicated hardware controller.
The ideal starter system for editing HD would be:
C:\ OS, programs and probably Windows Virtual Memory (Page File). This HDD can be smaller, but needs to be very fast.
D:\ Project files and PrE Scratch Disks. This needs to be larger, and speed is still important.
E:\ Media files in RAID 0 (2 physical HDD's stripped into a RAID 0 Array, and ideally managed through a dedicated controller card).
RAM will depend on the OS chosen. If 32-bit, filling up to 4GB would be good. If the OS is 64-bit, I'd recommend 12GB RAM.
Thank you! Tom