The integrated Intel HD3000 graphics usually performs on par with an ATI HD 5450/Nvidia GT220, on turboboost, so I wouldn't really consider it for a gaming computer. You can kinda overclock the 2600/2500 as well, but it has a locked multi so the only option is to run it with "turboboost" option, which is limited to around 4.2-4.3gHz and from my experience, those kinds of tools usually adds alot more heat than overclocking normally, since they tend to bump up the voltages quite a bit more than necessary. I'm not experienced with SB though so they might have refined the "noob overclocking utilities" a bit. There is no DX11 support in H67/P67Sandy Bridge IPG's, so if you want to play Cliffs of Dover in DX11, you can't. The only reason to why I'd pick the H67 is if I did lots of video encoding, film making etc. and not much gaming. The Sandy Bridge procs rule when it comes to converting/encoding because of the extra horsepower from the IGP.
It is a nice architecture and very flexible for the normal user, but if you run games at 1600x1200 and above, H67 will limit your options quite badly. You can also forget using much AA or AF with the integrated Sandy Bridge graphics. Especially AF. However, DirectX 11 and DirectX 10.1 graphics support is largely a moot point with regard to integrated graphics. Whatever GPU capabilities that are present in Sandy Bridge and Fusion, they are more suited to entry-level gaming and playing games from a generation or two ago rather than taking on top-tier DirectX 11 titles. For that task, using one or more high-end discrete graphics cards is highly recommended.
That's my 2 cents anyway.