I'm not a fan of either brand, or any other brand you'll find at Best Buy or it's compatriots. I'm more of a build it yourself or buy a Mac sort of person.
That all being said, the HP has a potential advantage in being a dual core chip, but the eMachines has a 64-bit chip. At the present time, both features are pretty much useless, however that may soon change.
Only the 64-bit version of Vista will be able to play back the new gen high def videos that you will be seeing in the form of HD-DVD and BluRay movie discs in coming months. However, a dual core chip is likely to last a little longer when it comes to raw performance. Especially as software developers get better about taking advantage of multi-core chips.
It's kind of a crapshoot either way, but either system will probably last you for a good 2-3 years if you aren't into gaming. If you plan on making ANY hardware alterations, aside from adding more RAM or another hard drive, then the eMachines would probably have an edge. With the HP being a Media Center PC, your hardware options are going to be limited significantly. More so by virtue of it being an HP, which has never been known for making systems that are easily customized. Neither company has exactly been known for producing high quality systems either. HP was a bottom feeder when it merged with Compaq, another bottom feeder, some years ago, and eMachines was right there with them before being bought by Gateway, which has been desperately clinging to life for years. They haven't done anything to improve the eMachines line that I've been able to tell.
Dell is a slightly better option, though they have a problem with large batches of systems having problems due to faulty components. I think the jury is still out on Lenovo's takeover of IBM's computer business.
Apple has always been a maker of high quality systems, though a Mac isn't always an option for some people. The Mac Mini's are great little systems. Small and quiet, they're essentially a headless laptop stuffed into a small desktop case. They're a little expensive, but you do get quite a bit for your money. And you can't find a better desktop OS on the market today than OS X. If you're looking for just a system for light office work, like word processing, and web browsing, it's hard to beat a Mini. They even make great home theater hubs, since they're small and quiet, they're easy to put somewhere out of the way, they don't make a lot of white noise due to fans keeping things cool, and they have one of the best remote systems of any home theater PC.
All of these are just some additional options to consider. It's your money, so get whichever sounds best to you.
Have to buy a new pc, Best Buy has 2 pc's in the price I am looking at $500-600 (tower only, I have a monitor etc.). They are emachines T6536 or HP Pavilion Media Center a1517x Desktop PC. Specs are:
PentiumD 805 (S) DC 2.66 GHz
1 GB memory
AMD Athlon? 64 Processor 3800+ 2.4GHz
Can't find any reviews on the HP product
Any input on choice would be much appreciated.