All passwords should be generated by a computer, because humans are very good at introducing patterns that weaken the result :-) If you have no trustworthy computer available, then literally using dice and the Diceware method for generating a wordlist/passphrase is a great alternative ... "a computer" doesn't have to be electronic!
Many passwords can be handled completely by a trustworthy password manager application, so that the human never needs to type those in. Choose as long and as complex a password as possible for each account, because you have no reason not to. 64 characters selected from upper, lower, numeric, punctuation and anything else the target account/site will accept will be overkill in terms of entropy, but it shouldn't matter because it's as easy for you to use as any other password. If the target has a shorter maximum length, just generate the longest they'll accept.
Some passwords are better off memorised by a human so they can type them in directly - e.g. the password manager unlock password, as well as others you might use regularly. These should be generated as word lists/passphrases, in the same manner that Diceware does. But your password manager should also be able to generate passphrases in this form, so you might as well use it.
For word lists/passphrases, you still have to worry about the length - but this is now a combination of the number of words and the size of the word list used. Diceware recommends a length of 6 words, larger lists can theoretically give you equivalent entropy with fewer words, but really we're now competing with human memory, which is actually pretty good, so again you should go with the longest passphrase that is practical to use.
In summary - there's nothing superior about passphrases compared to passwords in terms of math, but they are superior in terms of getting humans to effectively remember and input longer sequences of characters, and password security is basically all about length.
But it is overkill to sit there rolling dice if you have a trustworthy computer and password manager already available.