Google "How much DNA do we share with mice/rats?" From 90 to 99%, the same as with chimps. I've read too, that we share more in common with gorillas than chimps do with gorillas and that we share more DNA in common with them than chimps, by DNA percentage.
Many of these are science websites with no indoctrinating agenda that I can tell. I've no reason to doubt them, especially when they give the reason that it is why they experiment on mice and rats. They aren't just trying to eliminate disease in the mouse and rat population. I'd think Pandas, dogs/cats, and baby fur seals take priority with animal charities, rescues, and giving (just saying, again, I have not reason to doubt the percentages given).