Well, you're not missing much.
- The animation quality of Crash is inferior to eps. 5-6 of BGC.
- Due to her commitment as a rock singer, Kinuko Omori stepped down as the voice of Priss. She was replaced by J-Pop singer Ryoko Tachikawa. As a result, Priss' character gets screwed up and she betrays us by becoming an idol singer.
- No GENOM here. Not even an explanation of what happened to the corporation.
Of all the animated incarnations of BGC, Crash is the weakest. At least it's still better than Adam Warren's poor attempt at doing a BGC comic.
You forgot to mention the fact that Crash is mostly over the top silliness and has none of Crisis' edginess.