Man, this is such an old post... but someone shot me a link to this thread about this so I might as well post something.
From what I understand regarding the previous posts, nobody is really questioning how VVT-i and VTEC works, so far there's been a lot of good explanations of both...
But the real question is which is better, if I'm not mistaken.
To take this thread into a more non-technical direction, here are my experiences in very basic and crude terms.
The VVT-i system is something I wanted to play with a long time ago. When I messed with racing cams on my previous cars, I had to sacrifice some power from the low rpms to gain more at higher rpms. All those who changed out their stock cams to a racey cam would know this. An adjustable cam sprocket became very useful where I could tune and advance/retard to my liking but I often wondered how a fully automatic-adjusting cam gear would work on-the-fly. Back then, there were those cam sprockets that used centrifugal weights on springs, kind of like how a distributor advance mechanism works. This altered the cam "phasing" based on rpms. More advancing gained more power down low and retarding allowed for shifting the power peak upwards towards higher rpms. The VVT-i system is far more advanced but accomplished the same basic task to a much finer degree.
The result would be a much more smooth driveability and better overall street driving experience, which is why you can't "feel" it working. This is an example of linear power delivery.
VTEC on the other hand is a more radical experience having a clear "kick" when you rev it up. It's like having "turbo boost" on a normally aspirated car. I guess you can think of it like having a normal camshaft for street driving/fuel mileage AND having a race camshaft when you need it at the same time. With the help of modern technology, the engine is tuned differently for the experience on the low and high cams, and it would appear that the potential for making a lot of big power on top goes to the VTEC equipped car.
VTEC/VVTL-i having variable lift (pushing the valves open more) allows the car to breathe better and since an engine is basically a huge air pump... the more air that can be introduced/passed through, the more power will result from it. Normal VVT-i doesn't accomplish this effectively as the previously mentioned VTEC/VVTL-i.
So which is better? It depends on what you value more. A smooth power delivery that makes for comfortable street driving, or an experience involving a more radical driving experience with a kick... definitely not for grandma.