In short, ICE provides a smooth continuous panorama, but the most 3D model it will ever create is a bubble of photography which you are trapped in the middle of. If you only stand in one place and turn around to look in an outward circle, a panorama from ICE, Photoshop, or another panorama stitcher is appropriate, but this will never give you a 3D model, allow you to move around, or let you look at things from multiple different perspectives.
Photosynth is focused on presenting each individual photo just as it was taken, only arranged in 3D space and nested in the 3D point cloud of the scene. If you take care to scan different objects in the scene by taking photos around them and give the computer a tour of how to get from one thing to the next, you are free to move anywhere you like with confidence that Photosynth will follow you. Just remember to take photos close to each other. With the first steps into 3D stitching, you can rotate the point cloud to any angle.