Red striped Basculin are available only in White version, and blue striped Basculin can only be found in Black version. That's about it apart from colour.
No, it's the other way around. Also, they're not version exclusive. In Black I managed to find blue Basculin in bubbling water (or surfing spots as they're more commonly called), they're just rare. Here's an example for you. :3
Also there are a few physical differences between the colors. :D Their eye shape is different, so are their fins (red has spikey fins while blue has them flat and curving into a point), that also applies to the fin on their bellies as well as the fin just behind the dorsal (I think that's what the front-most fin on their back is called).
As far as stats go, I don't think there is any difference whatsoever, just the color variation.
I believe the blue Basculin also gets a different ability. Red gets Reckless and Adaptability, while Blue gets Reckless, Adaptability, and Rock Head. I think. Someone's gonna have to double check for me. ^^"
I firstly thought that could be a difference about stats (one more offensive or deffensive than the other), but if the only difference is at the ability, so I think that they're not that different besides the color, though.