After reading through most of that, it seems that the big problem with the XKCD scheme is that it's often impractical. Too many sites restrict password length and so you are forced to use the Schneier modification to get more entropy per character.

If you make a password from an alphabet of 64 characters (upper and lower case, digits, and some special characters), there are 6 bits per character of entropy so a ten character random password could have 60 bits of entropy.

If you are choosing words from a list 4000 words long, there are 11 bits of entropy per word and so you would need to string together five random words to get a password of equal strength. The big problem then is having enough space to type that many characters.