Well the first thing you have to choose is whether you want vista or not.The HP is lighter, has a higher resolution screen, xp professional,SD card slot, finger print reader and a longer warranty. The ASUS has a 20 GB larger HDD, express card slot (HP had the older PC card slot), DVI, and a webcam, and its cheaper. The graphics cards are nearly identical with the ASUS's being slightly better.
If you have the money and the stuff I listed under the ASUS are not essentials then go with the HP. HP's business line has excellent build quality, many claim the best, and will last many years. But I'm still not sold on Vista and simply being 1/2 pound lighter and the high res screen would be worth it IMHO.
However if you are on a budget and aren't willing to part with those 300 extra dollars the ASUS is still an excellent choice and a good deal, I paid around the same for my laptop last September and the ASUS would certainly beat it. Also keep in mind that 1GB of RAM is not that much in Vista where in XP its sufficient.