Both are plotless, Made up of short segments. They are about the hilarious happenings within their groups of friends. The both extreamly wacky but in a kind of relatable way. They both contain some pop culture references (although much more in Joshiraku).
Both shows are about a couple of students doing random stuff. they are both very funny and if you enjoy one of them the other will also be enjoyable. The one difference is that Plastic nee-san is about 3 girls and Daily Lives of High School Boys is about a group of boys.
Life is simply not worth living for down and out school teacher Itoshiki Nozomu. He has no hope of progress, no prospect of promotion, no chance at happiness… he is in despair! Even his name spells 'zetsubou' – 'despair', when compressed. But when the time comes to end it all, Itoshiki's attempted suicide on the first day of the new school year is foiled by relentlessly positive Fuura Kafuka. This saves Itoshiki long enough to meet his new class, and the quirky range of students under his care. Will Itoshiki Nozomu depress his students with his anguish? Or will Fuura show Zetsubou-sensei the joys of life and hope?
At the Kaimei Academy three classmates, “Bossun” Yusuke, “Onihime” Himeko and “Switch” Kazuyoshi have established their own club: the Academy Activity Support Club. Known as Sket-Dan for short, the trio accept any odd jobs that come their way in the name of maintaining a peaceful life for the students of the academy. Whether identifying a graffiti artist, fixing the school gym shed or helping a new student fend off his childhood bullies, no task is too big and no job too small for the Sket-Dan.
In the middle of class at a certain school, Rumi Yokoi, a diligent student, has her in-class life turned upside-down when her next-door desk mate "Seki" (full name Toshinari Seki) begins to play by himself at his desk in class. Although Yokoi is irked by Seki's distracting yet intricate playtime, she finds herself being drawn into his interesting hobby. Never being able to focus, Yokoi observes Seki's stunning ways of slacking off in class.
School life parody comedies that take fairly mundane situations and then take them to absurd extremes. These are both shows that draw the comedy out of ordinary situations. Neither show has a particular plot, but instead episodes are all made up of mostly standalone comedy sketches.
Tonari is short the episodes only contain one sketch. Daily Lives of High School Boys are full length episodes and each episode contain multiple sketches. Daily Lives also has a larger cast and lots of recurring jokes. Tonari is much more humble with most of the comedy being generated in the minds of the characters. It also has a small cast of two characters.
However, both shows are good examples of random comedy. If you like one then check out the other.