A few generalities may apply here:
.
It is generally the case that Knoppix is used as a LiveCD LiveUSB,
or in a poor-man's HDD install,
where Debian is more often used in a 'permanent' HDD install.
Knoppix is probably the best distribution of ANY, in regard to
hardware recognition; more likely to JUST WORK with any
keyboard/video/graphics/wifi combination than any other distribution.
It follows that, given the same hardware to work with,
Knoppix makes it easier for a novice to get a working linux.
Debian MAY be more suitable for advanced users to tailor
to their specific needs.
Knoppix is not limited to 32-bits-only; however, most linux users would be
hard put to demonstrate a common and significant use or situation
where 64-bits offers anything more than a MODEST capability improvement;
notable exceptions being re-mastering and/or working with file SIZES
greater than 4 Gb.