Live Color is about moving groups of swatches around as a group - it's not for bitmapped images at all. For example, I can grab a group of swatches such as the group I tend to use for Illustrator graphics that are headed into Powerpoint - and rotate the whole lot in hue in one go, watching the results as I do. If you were to do that in Photoshop, you'd use a Hue / Saturation Adjustment Layer or similar (though there far more powerful Hue / Saturation / Brightness adjustment tools in Camera Raw 4 and Lightroom).
I have the entire Creative Suite 3 Design Premium on my machine these days (sadly, since buying and installing the CS3 upgrade I've had to spend more time working in Illustrator and InDesign than playing in Photoshop). You can access some bitmap filters in Illustrator - but they're only a subset of what's in Photoshop, and by no means make up a complete solution.
Indeed, I'd go as far as to say that Illustrator is completely unsuitable as a photo tool; indeed, if you want to do much to a photo, you land up placing it as a Photoshop object in either Illustrator or InDesign, or creating a TIFF or JPEG and using that. It's much the same as there's some paths functionality in Photoshop, but you really can't use Photoshop for vector art.
David