The P6200 and the slowest mobile i3 (i3-330M) are essentially the same except the P6200 loses hyperthreading, SSE4.x instructions, virtualization support, and has higher core voltage (potentially more battery usage).
Which i3 are you looking at? Any i3 above the 330M will get you increased clock speed too. The lack of the Hyperthreading feature is the big loss if you go P6200.
The upgraded HDD does make a difference, but I haven't don't solid benchmarks to figure out how much. If what you're doing is disk dependent or processor/threadding dependent... that could drive you either way. You have a decent amount of memory, or else HDD speeds swapping pages in and out of memory would play a role in general responseiveness.
A 7200rpm 500 GB drive by itself is going for $66 at Newegg. It looks like the HP can be configured for 7200rpm and a 2.4 GHz i3 for $530. The links aren't working for me now... or else I'd check the prices of the others.
Given those choices I would go with the HP. Asus is a good brand and I just don't like gateway. With the HP you can do the customization - I would go with the i5 460 because of the increased clock speed and turbo boost. (I looked them up at the Intel site and they're all 32nm, all 35w TPD. The biggest difference I saw was both the i series have 2 cores and 4 threads.) The HP also has the FREE Upgrade to 4GB DDR3 System Memory (1 Dimm), so that should leave you with another slot that you can fill later giving you 8 gigs of memory. Also, I would go with any of the 7200 rpm hdd's - whatever size you require for your needs. As for the video??? If you really only use it for a regular home/office laptop then the onboard HD graphics are fine. You can even plug it up to a small tv/monitor and watch in HD with the HDMI plug that comes standard. The only thing about the onboard is that it uses your ram as video memory, not a big deal if it's a work laptop.