You'll have more options with Dell, unless you decide to go with the "Compaq" arm of HP.
As far as choosing between the two, there really isn't anything distinctive about either manufacturer. They pretty much use the same components, offer the same quality of product and support (terrible). Both manufacturers have their higher end laptops and their lower end ones... In that respect, you usually get what you pay for. $600 is a good mark to get a decent budget laptop.
The only difference is really appearance and packaging. Just find the laptop that is the right size, right speed and right price for you. Don't pay too much attention to the brands.