First, I'm a KofC and a Mason.
Second, the KofC is a Fraternal Insurance Society and has a AAA Best rating for it's life insurance products. In that way, it is VERY different from Masonry. It was founded in 1882 so that Catholic men would have a way to meet together (as many fraternal organizations were springing up at the same time). The article linked previously (post #13 got that much right). The rituals linked are nothing like the KofC ceremonials of today (sorry to burst anyone's bubble), and they have changed quite a bit since I joined the order in 1988, and even more from when my late father joined in the 1960's. The KofC ceremonials are changed regularly, unlike Masonic ritual.
Third, good luck getting a copy of the ceremonial books. Ceremonial books are sent to each Council by Supreme and have serial numbers so if any goes missing, the Council gets charged a fee for losing them, and another fee to replace them. Ceremonials are not emphasized very much in the KofC...most members don't know any of the degree parts, or even remember much about the degrees.
Fourth, as a former KT, and 4th Degree KofC, about the only thing similar between the two sets of regalia is the sword and chapeaux. The KofC 4th Degree uniform is a plain black tuxedo, sword, baldric, cape, gloves, and chapeaux. The KofC touts itself as an organization of Catholic gentlemen and the 4th Degree regalia is intended to reflect that. The KT uniform is (at least when I was active) is an actual military uniform (Coast Guard jacket, as I recall) with the sword worn from a military-styled belt and no cape. The Masonic KT (if I remember correctly) is a soldier for Christ and the regalia reflects that.
Fifth, I've not know any Council's to work with the Mason's, but I get the impression that they would if the occasion arose.
I hope I've been able to help anyone and I also hope I haven't been very off putting by my tone.