Hello, I'd forget the Intel Graphics, always first to be droped by OSX & High end Apps.
That being said...
You can see the results on this benchmark site. Do a search using Ctrl+F to find the cards.
In simple terms the HD 3000 is the 354th most powerful graphics card you can get.
The 6630M is the 271st most powerful.
and the HD 4000 is 269th most powerful card you can buy. So not much between that and the 6630M really. I don't think you can get his on the current mac mini though.
I think the benchmark is raw processing power of the GPU, not how the cards deal with specific video features. Could be wrong though.
Personally I would get the 6630M. You will probably get more life out of our mini. Unlike a pc, you can't just swap it in the future when things start to struggle a bit.
Mac mini "Core i5" 2.5 (Late 2012)... Geekbench: 6643/7469
Mac mini "Core i7" 2.6 (Late 2012)... Geekbench: 11367/12807
If you are editing video the quad core Macs are the better choice. As for Intel graphics, for normal use - i.e. watching movies, streaming video, playing typical, non-demanding games, they are excellent. Highly GPU-intensive games get decent marks. There has to be some more reviews of using FCP on a HD4000 graphics out there, but I do not have personal experience to recommend one over the other. If in doubt, the video card is always a better choice, even if it means buying a used or refurbed 2011 mini or iMac instead.
P.S., the 2012 mini's are HD4000 only, there isn't any version with a dedicated GPU. So if you want a mini, the 2011 base and mid range models are your best choices. If you do get a 2012 mini (or any Mac with HD4000 graphics), max out the RAM. The Mac will assign more dedicated RAM to the GPU with maxed out RAM.
Here is another thread on your question but not many replies yet (it's recent):
Thanks a lot for the lucid explanation. i understand the issue much better. Got lucky today also, ended up getting a used 27" iMac, Duo Core, 2009-10, with Radeon 4670 video, 256mb. Though older and slower, I needed some of port features, and it's plenty fast for doing the video graphics I need to do. Plus, It's loaded with software that i would have bought, Adobe CS, Final Cut Pro, etc. Saved money to get other hardware.