In terms of performance (especially in gaming) the AMD Athlon 64 has always been superior to the Intel P4 in most catagories. Just look at the Benchmarks.
*Note that the first system I showed you had the Athlon 64 3400+ and the other was the 3500+.
Intel has got caught in the clockspeed war, thinking that more clockspeed equals faster cpu. That is not true. Without getting technical, AMD has found otherways to find performance with their chips design such as a fast FSB (Front Side Bus). The best cpu out there is an AMD FX-57, not an Intel. If you want some technical stuff read this Discussion
Also note that the P4 in your Dell does not have 64-bit capability which will be necessary for future applications. In other words, the Emachines will last longer.
In regards to the warranty, all Emachines feature a 1 year limited warranty that feature,
1. One-year guarantee on Parts and Labor.
2. One-year technical support via telephone.
You can read about it http://www.emachines.com/support/warranty_info.html#std_warr
If 1 year isn't long enough for you, you can purchase an extended warranty through Emachines. Just scroll down on that page.
Also, Circuitcity and Bestbuy will offer their own warranties to you as well. Either way your covered.
IMO if your computer has faulty hardware or software you will see a problem within 1 year and extended waranties are unnecessary. If you take care of your computer you will not need it.
Also, note that if you buy a Dell printer ink is not popular in stores such as Staples, Officemax, and Walmart. So you will need to buy your ink online if you buy a Dell printer.
Those computers are both in the $1000 range but with rebates they are within your budget.