CIO Magazine (Via Information Week) came up with 8 reasons to pick the BlackBerry Storm instead of the Apple iPhone 3G.
The advantages of the Storm mentioned are:
Stereo Bluetooth
Removable battery
Expandable memory
Digital camera, video recording
Storm works as a tethered modem
Touch screen provides tactile feedback
Cut-and-paste
Multitasking champ

These points are all more or less valid, but the list misses several comparison points. Most prominently the Apple iTunes App Store that allows iPhone users to choose between tons of great applications and games. RIM has announced an BlackBerry Store, but it still has to be seen if it will catch on like the iPhone App store did.
Of course also quite an advantage is the iTunes music and video infrastructure that makes the iPhone a complete iPod that so many are used to.

The BlackBerry Storm is sure the most valid contender to the iPhone, but if pressed I actually still would pick the iPhone.
More BlackBerry Storm News.