No. Is the simple answer.
They're not terribly equivalent. Why is your Comp Sci degree in Arts and not Science? What was your GPA? How "good" is the school you went to?
A First is the highest degree
2:1 (upper second) is next
2:2 (lower second) is an average degree
A third is the lowest
Honours suggests a better school/degree program. Sometimes students who are not doing so well are allowed to continue but they move to a regular degree rather than an honours one. I think the US equivalent maybe less credits being required for the degree. UK degrees don't really work on the credits system (or didn't when I was there), so that is why comparisons are so hard. Also UK students specialize much earlier than UK students, so there are not so many course requirements in field outside of their major and minor focuses, although my uni was trying to change this a little when I was a TA there.
Typically to get a first, you have to score above 70% in all exams, papers etc. Exams are generally designed so that to get a 100% you'd have to be a bloody genius. ymmv and it's been a few years since I was there -things are being more standardized and some suggest "dumbed down".
I think someone came up with a rough conversion on one of the expat sites I visit. I'll go see what I can dredge up.......