Which is a faster extraction method?

both would be better on the faster PC. although you might have to reformat your USB to carry some files over

Edit: oh read wrong. directly from USB...not sure never exactly tried that before

I would say that the main factor would be where will you be saving the extracted file. If you're extracting to your hard drive, it won't make much of a difference. You won't notice the difference anyway, unless the file is way too big, because most of the time will be spent on the decompression itself, not on IO.

Why don't you conduct the experiment yourself?

I was going to say "anally" but then I read the rest of the post.

i would say, copy the archive to your pc and then extract the files.

Extract from USB to HDD.
This eliminates need to write rar to (slow) disk and then potentially read & write from same disk.

Techical reason, simplified, not whole file is read to memory on single time, but on smaller pieces.

Directly from USB:

Read to memory
Unpack
Write

Copy to HDD, extract from there

Read to memory (from USB)
Write to disk
Read to memory (from disk)
Unpack
Write

As you can see there are more steps needed.

Additionally same drive extraction results in following operations

(seek)
(read)
(seek)
(write)
(seek)
(read)
(seek)
(write)

When different source than destination drive

HDD USB
(seek) (seek)
(write) (read)
(write) (read)

As you can see this is much shorten than above, since we can do these in parallel and don't get penalties from extra seeks.