The lighting on the CGI version is brighter (and looks to be from multiple sources) as opposed to the "original" footage, where the image is darker. This comparison is in contrast to other comparisons I've noted, where the TOS-R Enterprise is darker than the "original".
It seems whenever the lighting on the TOS-R spacecraft gets brighter and more thorough (more sources), it ruins the CGI image.
The state of CGI rendering at the time TOS-R was done was just a little too primitive, cutting into the available budget. As such MOST of the lighting looks wrong, in some places very
noticeably so. Your comparison shots exemplify this well.
In reality, any time the Enterprise is viewed in deep space it would be barely visible (aside from lit windows, running lights, and nacelle caps), because there is NO LIGHT SOURCE aside from the distant stars. Any time it is in a solar system, it would have to be lit up by ONE light source, not multiple. TOS-R should have actually tried to darken shots of the Enterprise, rather than lighten them. I'm not saying they should try making it completely realistic, because it wouldn't look good and detract too much from the original series. Going slightly darker rather than prominently brighter would have been a good thing.