Bravia Engine doesn't do that much much. I've got a Neo, has it on board, hardly ever notice it.
thing it does is improve things (images and movies) you watch in the Android Gallery slightly. It increases the contrast, and fixes the colors. It looks really good on some images, makes other images slightly worse. The best improvement is for video, and does (as far as I know) have effect on every video that uses the built-in player (so not Youtube, but when you click a video link in the browser it should, for example).
The effect can be seen very clearly on in-phone screenshots. Open each image in a new tab and then switch between the tabs to really see the difference. Example of http://interfacelift.com/wallpaper/d.../symbolic.html
with Bravia Engine <-> without Bravia Engine
With Bravia Engine (above), without Bravia Engine (below)
Again, as you can see, it's mainly the colours that are just so much better, like.no.other if you know what I mean :P