The Sony C1VE Picturebook is the first Vaio to be fitted with a Transmeta Crusoe processor.
According to Linux, its 600MHz provide a sufficient power of around 1199 BogoMips, once installed.
The C1VE also benefit from its Crusoe in terms of autonomy but, disappointingly, it won't exceed 2,5 hours of battery-life. Anyway this machine is relatively cheap regarding its possibilties.

2.5 hours of battery life certainly is not good, although you can buy a much larger battery for it which fits clumsily onto the back. It costs about £280 in the UK and is not sold in any of the Sony shops I have been to, so must be ordered directly from their warehouses.
The larger battery allows for about 14 hours' typing/noding, or 7 hours playing Unreal Tournament (unadvisable) or watching videos.

Incidentally, this is about one of the best machines for watching videos on on the move. It has no DVD drive, but using DivX compression you can fit about fifteen films at high quality onto its hard drive (12Gb). Playback works wonderfully, and the screen is very nearly the correct ratio for feature films.