I recently set up a system to do this and it works great. The key components are getting the Video from the console into the PC and also being able to record the video to the hard drive in real time.
I used an HDMI splitter box (cost around ?50) to take the video to the PC. I used a
Blackmagic Intensity Pro capture card with its bundled software to record the video. (I could have saved on the cost of the splitter box as the card allows the video signal to be looped through but this would have meant that I would have had to have the PC on whenever the XBox or PS3 were in use.)
In order to record, disk write speeds have to be fast. I found that the cheapest and best way to do this was to create a RAM drive. I used some software from Dataram to create this RAM disk. (I think that this is always going to be the best solution as the actual data transfer rate for Magnetic hard drives have not increased in 10 years meaning that the latest SATA III drives are no faster than the old E-IDE ones! The data transfer rates are still only around 110MB/s even though the SATA III standard allows for 600MB/s. SDD's are now approaching this max speed. A RAM drive however is many times faster than even an SSD and is therefore the best choice for any process that will involve a lot of disk access. (I installed extra RAM so that I could devote some for the RAM drive when needed.)
I did find that the best I could record was 1080i and not 1080p. This may be a limitation with either the Blackmagic card or bundled software, though it is advertised as being capable of 1080p. This was my only minor issue. ( I did check that it was not the splitter's fault by wiring direct.) The Blackmagic Express software produced the warning "No Remote" any time the input signal was 1080p.
I hope that this helps someone else.