Heck, the Federation in TOS doesn't even believe in punishment as a concept - criminals only ever get therapy (even if it sometimes requires locking them up for a while). And even in DS9, punishment only ever touches non-Feds, and then Richard Bashir who committed an ancient crime and violated a strong human taboo.
Any comparison of justice systems would be highly asymmetric, then, regardless of the partner in the extradition treaty. I'm sure there's a host of death penalties in Klingon law in the 24th century, too, yet there's an extradition treaty there as well ("Rules of Engagement"). We don't know if that one is unilateral or bilateral, but I could well see the Klingons refusing to sign for the latter when they familiarize themselves with the barbaric UFP practices of imprisonment and brainwashing, and the inability to defend one's case through a perfectly fair duel.
Timo Saloniemi