In gaming performance, yes. In some other applications the Gateway model will perform better due to the CPU.
The Gateway has a somewhat better CPU, they are equal in performance for RAM, hard drive, optical drive, media reader, but the 8600GT video card on the Gateway system is entry level gaming performance. The 9800GT card on that HP system will easily run rings around it. Gateway is a good brand and the system is fundamentally sound, it's just neutered in gaming performance with that 8600GT GPU.
Another option is this model by Gateway....
Gateway Official Site: Store - FX541X, Desktops, Product Details
Same solid core, but with an acceptable gaming GPU in the 8800GT. Of course, the price is a good bit higher than the HP even without a monitor. So, if I were in your position I would opt for the HP system with the 9800GT GPU.