Looking at Shizuo's page, it seem that even after taking out the ridiculous powerscaling that was being done from an apparent joke route from a non-canon game to a character from another series (Level 6 Shift Mikoto... yeah, that was complete nonsense made up for wanking Shizuo) he is being scaled to Celty. Which normally would be fine, since Celty is just slightly superhuman and she considers herself to be weaker than him, except that for some reason she got put as 8-A for what looks to be just a range feat, not AP.
In general the 4 Durarara's pages here need to be revised, a lot of powerscaling and feats seem weird now that I look at them. Simon and Izaya can fight a non-serious Shizuo and they are supposed to be just strong normal humans (at least as normal as a human being can be in Durarara). Unless the LNs go about things a lot differently after the parts I read (volumes 4 to 6, so it is possible) they don't seem like Building level characters, as Shizuo is still threatened and hurt by normal guns, a normal guy stabbing him with a special pen, the Saika army cutting him with their knives, a ballistic knife and even a box of knives falling from a shelf into his back. None of those things are Building level. Shizuo is consistently hurt by this kind of stuff, he just shrugs them off because of his insane stamina and resistance to pain.
I've heard of the comparison of Claire and Shizuo before (haven't seen Bacanno yet, intending to do so when I have the time, so I can't say if it sounds reasonable), but it's usually with the comparison/tier list fans post around without a source, like the thing that was added to Shizuo's page of him being on par with a demon. So it would be best to post the source of the statement, but if Clair is considered to be able to fight on par with Shizuo and his stats here are accurate, it makes me doubt Shizuo's stats here even more.